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Vol. 37 







FROM MAY, 1901, TO MAY, 1902. 



SSttibrrsitg $3rcss: 
John Wilson and Son, Cambridge, U.S.A. 




I. The Possible Significance of Changing Atomic Volume. By 

Theodore William Richards 1 

II. Preliminary Diagnoses of Neiv Species of Laboulbeniacae. — IV. 

By Roland Thaxter 19 

III. The Law of Physico- Chemical Change. By Gilbert Newton 

Lewis 47 

IV. The Visible Radiation from Carbon. By Edward L. Nichols . 71 
V. On Ruled Loci in n-Fold Space. By Halcott C. Moreno . 119 

VI. The Arc Spectrum of Hydrogen. By O. II. Basquin .... 159 

VII. The Standard of Atomic Weights. By Theodore William 

Richards 175 

VIII. Stuilies on the Reactions of Limax maximus to Directive Stimuli. 

By Peter Frandsen 183 

IX. The Algae of Jamaica. By Frank Shipley Collins . . . 229 

X. Modifications of HempeVs Gas-Apparatus. By Theodore Wil- 
liam Richards 271 

XI. The Parametric Representation of the Neighborhoo<l of a Singular 

Point of an Analytic Surface. By C. W. M. Black . . . 279 

XII. A Preliminary Enumeration of the Sorophorcae, By Edgar W. 

Olive 331 

XIII. The Decomposition of Mercurous Chloride by Dissolved Chlorides : 

A Contribution to the Study of Concentrated Solutions. By 
Theodore William Richards and Ebenezer Henry 
Archibald 345 

XIV. A New Investigation Concerning the Atomic Weight of Uranium. 

By Theodore William Richards and Benjamin Shores 
Merigold .... 363 

XV. The Significance of Changing Atomic Volume. II. — The Prob- 
able Source of the Heat of Chemical Combination, and a New 
Atomic Hypothesis. By Theodore William Richards . ;>!»7 




XVI. On the Accuracy of the Improved Voltameter. By Theodore 

William Richards and George W. Heimrod . . . 413 

XVII. 1. The Northern Carices of the Section Hyparrhenae. 

2. The Variation of Some Boreal Carices. By M. L. Fernald 445 

XVIII. Apatite from Minot, Maine. By John E. Wolff and 

Charles Palache 515 

XIX. A Description of Epidote Crystals from Alaska. By Charles 

Palache . 529 

XX. On the Specific Heats and the Heat of Vaporization of the Par- 
affine and Methylene Hydrocarbons. By Charles F. 

Mabery and Albert H. Goldstein 537 

XXI. Certain Sense Organs of the Proboscis of the Polychaetous A nne- 

lid Rhynchobolus dibranchiatus. By Adele Oppenheimer 551 

XXII. The Composition of Petroleum. By Charles F. Mabery . 563 

Records of Meetings 599 

A Table of Atomic Weights. By Theodore William Richards . . 630 

Report of the Council 635 

Biographical Notices 635 

Augustus Lowell 635 

Truman Henry Safford 654 

Horace Elisha Scudder 657 

Joseph Henry Thayer 661 

John Fiske 665 

James Bradley Thayer 679 

Officers and Committees for 1902-1903 683 

List of the Fellows and Foreign Honorary Members . . . 685 

Statutes and Standing Votes 693 

Rumford Premium • 703 

Index 705 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 1. —Jink, 1901. 


By Theodore William Richards. 


By Theodore William Richards. 

Presented May 8, 1901. Received April 16, 1901. 

Compressibility is a universal property of matter. It is so essential 
an attribute of the experimental universe that it is ascribed even to the 
imponderable and imaginary ether as well as to " material." The three 
states of matter are compressible in very varying degrees, dilute gases 
being compressible to a great extent, highly compressed gases and liquids 
to a far less extent, and solids to an extent usually even less than liquids. 
The first case has been studied in great detail, the last two scarcely at all. 

Compressibility is simply an evidence of work done upon a system by 
a given pressure. It' the application of considerable pressure in a system 
causes only a slight change of volume, it is evident that there must be 
other powerful influences at work. Clearly a clue as to the variation in 
these influences can be found in the quantitative study of the phenomena. 

In all reversible cases which may be studied directly, an increase in 
pressure is accompanied by an increase of resistance to pressure and a 
diminution of volume. This depends upon the fundamental idea of 
equilibrium, and is a special case of the general principle sometimes 
named after Le Chatelier. Working backwards from this idea, one may 
infer with regard to any given substance at a given temperature, that it 
is under the influence of great pressure if its volume-change is unusually 
small under addition of a given pressure. 

There are two conceivable causes of great compression in a substance. 
The pressure may be applied from the outside, or it may be due to the 
mutual internal attraction or affinity of the smallest particles of the 
substance for one another. That is, the substance may be compressed 
either by an outside pressure, or by the intensity of its own cohesion. 
The first may be typified by highly compressed gases, the second by 
liquids, whose small compressibility may be taken as evidence of great 


In solids one must consider also the directive agency which manifests 
itself in crystalline form and optical structure. In a few cases the 
" crystallogenic force" seems to be rather directive than attractive; in 
other cases it seems to have both properties, for considerable diminution 
in volume may occur. The presence of the crystal-making force compli- 
cates the phenomena and is a considerable stumbling-block in the way 
of the study of the internal tension of solids. 

In view of these facts, it seemed to me possible that the study of com- 
pression as manifested by atomic volume under different circumstances, as 
well as of atomic compressibility, might afford some light as to the 
affinities at work. The attempt, while only just begun, has not been 
wholly unsuccessful. 

Evidently the liquid is the most suitable state in which to study the 
effects of molecular and atomic compressibility. It is most suitable 
because the irregularities in the behavior of liquids are very great, indi- 
cating various internal stresses, and because they are nevertheless not at 
the mercy of the directive crystal-making tendency which superposes its own 
influence upon that of cohesion. The great difficulty in the subject lies 
in the fact that the total compressibility of a substance is usually made 
up of a number of parts ; the molecular compressibility might be due 
partly to a diminishing of the so-called " free-space" between the mole- 
cules, as well as to a diminishing of the distance between the atomic 
centres. In words free from hypothesis, we may say that the compressi- 
bility may be made up of a chemical and a physical compressibility. 
When one comes to compute from compressibility the probable affinities, 
one is still more at a loss, — for each affinity is a mutual affair, concern- 
ing two specific substances. The immense number of variables thus 
introduced has discouraged most investigators, and I can find little if any 
hint of the significance of chemical compressibility in the literature 
familiar to me.* 

In a case of this kind, one naturally seeks at first cases as simple as 
possible. A study of the volume changes which take place on mixing 
liquids reveals at first no apparent regularity. In some cases an expan- 
sion occurs, but more usually a contraction ; sometimes heat is evolved, 
and at other times heat is absorbed. One law may, I think, be detected 
in the midst of the confusion, namely : Similar liquids exhibit less 
change of volume on mixing than dissimilar ones do. That is, where the 

* The considerations of NordenskjiJld are too seriously complicated by uncer- 
tain assumptions to liave much value. (See Ostwald's Lehrbuch, I. 850 (1891), for 
these and similar considerations.) 



affinity of a substance for itself is not unlike that of the substance for 
another, no great contraction or expansion occurs on mixing. Thus 
benzol and tuluol when mixed scarcely change in volume at all, while 
alcohol and water contract considerably. That is just what would be 
expected if affinity is the cause of contraction. 

In order to use such facts it is not necessary to imagine an atomic 
theory adapted to them. Such a theory is ventured upon at the end of 
this paper, but the facts are significant without it. One only has to bear 
in mind that liquid and solid substances resist compression, and hence 
that when we find them compressed we have reason to believe that 
pressure has been applied upon them. It is rather a matter of common 
sense than a hypothetical abstract conception. 

In order to present in a clear light the complications iuvolved in the 
study of even a simple series of cases of chemical compression, the facts 
concerning the molecular volumes of several metals and their oxides are 
recorded and discussed below. 

Molecular Volumes of Oxides. 


Weight of 
metal com- 
bined with 
16 grains 





Space oc- 
cupied by 
giveu weight 
of metal. 

Space oc- 
cupied by 
weight of 

Excess of 
of oxide. 

2 Ag . . . 













+ 4.7 

Cu . . . . 






+ 5.3 

Ni .... 






+ 5.15 

Cd . . . . 






+ 6.75 

Zn . . . . 






+ 5.0 

Mg .... 






- 2.0 

2Na ... 







2 II ... 







Si .... 






+ 6.0 

In compounds of carbon, accon 

ing to posi 

... 4.' 

' to 12.0 

In liquid oxygen at —119° and i 

)0 atm. (s] 

). gr. = 0.6, 

5). . • O 

= 24.5 c.c. 

In liquid oxygen at —181° and ] 

. . . O: 

= 14.1 c.c. 


While in the first part of this paper no atomic hypothesis is assumed, 
the words atomic volume, atomic weight, and atomic heat will be used in 
a purely material sense, as the actual constants pertaining to quantities 
chemically consistent. 

The results recorded in this table are typical of the variety of degrees 
of contraction which take place when substances combine with oxygen. 
It is evident that in some cases the product occupies considerably more 
space thau the metal from which it was formed, and that in others 
(typified by magnesium and sodium above) the oxide occupies consid- 
erably less space than the metal. This last remarkable circumstance 
at once emphasizes the absurdity of estimating the atomic volume of an 
element in a compound by discovering the volume-change which takes 
place when that element is replaced by another. Oxygen cannot be 
said to occupy a minus quantity of space, — the only possible outcome 
of the false assumption in this particular case. The false method gives 
fairly consistent results among carbon compounds only because of the 
great similarity of their composition. This consideration leads to the 
first law underlying the change of volume in chemical or physical 
change, namely, The atomic volume is not a constant, but is dependent 
upon the environment. This law was first suggested by Horstmann,* 
but he looked upon it rather as the absence of a law than as the 
presence of one. 

If the affinity of oxygen for the metal were the only variable entering 
into the figures given above, it is obvious that the total contraction, 
the difference between the volumes of factors and product, would be at 
once a comparative measure of the attractive forces which produce the 
compression. This reasoning of course rests upon the plausible ground 
that a state of being which resists pressure, such as liquid oxygen or 
solid metal, may be compressed only by the application of pressure. 
In this case pressure may be supposed to be applied by the mutual 
affinity. But unfortunately the case is not so simple. 

It is clear that in each case recorded above at least three affinities are 
concerned : first, the affinity of the metal for itself; second, the 
affinity of oxygen for itself ; and third, affinity of the metal for 
oxygen. The second of these is constant throughout the series, hence 
for the present comparison it may be considered as a known quantity. 
Therefore each change of volume may concern at least two unknown 
quantities. Hence if it were possible to measure either of the two 

* Horstmann, Ostwald's Lehrbuch, I. 389 (1891). 


variable affinities, an approximate idea could be obtained concerning 
the other from these data concerning atomic and molecular volume. 

A slight uncertainty is caused also by the possible varying intensity 
of the u crystal-making tendency " which determines the structure of 
solids. The small differences caused by this uncertainty may be seen 
from the following typical calculation. If solid rather than liquid 
mercury had been chosen above, the atomic volume of the mercury 

would have become — — — = 14.2 instead of 14.7, and the excess of 


volume of the oxide would have been 5.2 instead of 4.7. These 

differences are unimportant compared with the larger values under 

consideration ; the precise state of the solids or liquids makes less 

difference than one would have supposed. 

Is there any direct method of determining either the mutual affinity of 
the two elements or the affinity of the metal for itself? 

Countless attempts to measure the former have so continually resulted 
in failure that many chemists are inclined to deny the existence of 
chemical affinity. The electrometric method suggested by Ostwald * 
clearly measures one of the ways in which chemical affinity may accom- 
plish work, but it is limited in application and only represents a small 
fraction of the possibilities. The thermal relations are complicated by 
well-known thermodynamic irregularities, and would be fully significant 
only at the imaginary absolute zero. 

The direct determination of the affinity of a substance for itself is an 
easier matter, for many of the properties of a single substance, such as 
volume, compressibility, tenacity, must be associated with this affinity. 
Let us seek to study these relationships more closely. 

If one could only be sure that all substances, when relieved of their 
self-affinity, would occupy the same volume, the atomic volume itself 
would be the simplest and most direct means of comparing this property 
in different substances. The smaller the actual atomic volume,- the 
greater must be the self-affinity. Such an assumption would at first 
sight seem to be justified, for those elements which have the largest 
atomic volumes have the least inclination to remain in the elementary 
states. Deserting the elementary state means introducing other affini- 
ties, however ; hence the assumption would be unsafe. 

It has been already pointed out that compressibility, if measured over 
a wide range of pressures, might afford a clue to the extent of compres- 

I tstwald, The Chemometer, Z. phys. Cheni. 15, 399 (1894). 


sion already existing in any given substance. But the comparison of 

different substances involves the dangerous assumption that all substances 

would be alike compressible if freed from self-affinity, — an assumption 

which seems more probable than the last, but which nevertheless must 

be rejected. A much safer measure of the stress under which a single 

substance rests is the work which heat is able to do upon it. The 

changing of a simple substance from t° to t° + dt° Centigrade must 

involve the addition to it of an amount of internal work which is 

represented by the rise of temperature multiplied by the heat capacity 

of the substance, or C dt. In a simple elementary substance, when this 

work does not involve the alteration of crystalline form or any other 

apparent change except increase in size, it seems reasonable to consider 

no other variables, at least as a working hypothesis. If this is the case, 

we may write C dt = P dc, in which P is the internal stress against 

which the heat-energy is doing work, G the molecular heat capacity, t 

temperature, and v volume. The stress against which this work is 

being done is due only to the internal stress and to atmospheric pressure 

(which latter may be neglected by comparison with the very large value 

G dt 
of the former), hence the stress = P =— — ■• This can apply precisely 

only to infinitesimal changes, because in all probability P will vary with 
the volume. While it cannot be claimed that the expression just given 
certainly expresses a single pressure pitted against temperature-work, the 
expression certainly represents a resultant tendency which opposes 
expansion by heat, and therefore, by inference, opposes all other forms of 
expansion.* It is the inward tendency, the opposite to the driving 
tendency f or fugacity.J 

While then this stress, represented by the quotient of energy divided 
by change of volume, can hardly represent anything very definite, it 
must nevertheless be supposed in a general way to increase when the 
self-affinity increases. Hence, while giving no certain knowledge, its 
study may give an indication of affinity. 

A typical comparison may be made of the two elements zinc and 
mercury. They are simple, similar, and yet widely different as to their 
power of holding oxygen. In each case the atomic contraction on union 
with oxygen is about the same. If we take as the atomic volume of 

* All the slight data which we possess upon compressibility seem to run 
parallel with the coefficients of expansion. 
1- Richards, These Proceedings, 35, 471. 
% Lewis. 


oxygen the atomic critical volume, the contractions are as follows : 
14.7 -f 24.5 — 19.4 = 19.8, in the case of mercury, and 9.5 + 24.5 — 
14.5 = 19.5, in the case of zinc. If the metals were originally subject 
to the same internal stress, we should infer from the similarity of con- 
tractions that the affinities concerned in the two cases were about equal. 
This inference is, however, overthrown by other facts. Both elements 
have about the same atomic heat capacity, hence no internal rearrange- 
ment takes place in one which is not approximated in the other. On 
the other hand, the increase in atomic volume for a rise of 1° of tem- 
perature exhibited by one is much greater than that exhibited by the 

If a gram atom of one element increases more rapidly in size than 
the gram atom of another, it is only reasonable to suppose that the 
heat energy is finding less opposition in the former case. The co- 
efficient of cubic expansion of mercury is 0.000179 at 0°C. and the 
heat required to raise a gram through 1° is 0.139 joule. With zinc 
the corresponding numbers are 0.000087 and 0.392. * The respective 
atomic volumes are 14.7 and 9.5. Substituting these values in the 
equation we obtain. 

p (200X0.139) _... , 

" = (14.7 X 0.000179) = 106 ' 000 me g ad y nes Per square cm. 

(65 4x0 392) 
Pzn = (9.5 x 0.000087) = 310 ' 000 megadynes per square cm. 

Both these pressures are very large, for a megadyne exerts on a 
square centimeter a pressure of almost an atmosphere. As has been 
said, they signify a resultant tendency which resists expansion. 

It is interesting to note that these stresses agree in their indications 
with the comparison of boiling points and latent heats of evaporation. 
The boiling point of mercury is 357° C. and that of zinc about 930° C. 
The latent heat of evaporation of zinc is not known, but there is no 
reason for believing that in its case Trouton's rule is broken. Hence 
the criteria all indicate that zinc is harder to dissociate from itself than 
mercury is. 

A comparison of the energy-quotients of several metals, measured in 
this way, may be of interest. 

* All figures not otherwise designated were taken from the tables of Landolt 
and Burnstein, 1894. 



(in order of 
boiling point). 

Boiling point 

Heat capacity 
(,mayers per 



of expansion. 

Energy quotieut 

P _ cat 

atom, expan. 

mol. weight. 

Mercury . . 
Cadmium . 
Sodium . . 
Zinc .... 
Copper . . . 
Lead .... 

357° C = 630° A 

770° C = 1043° A 

860° C = 1133° A 

930° C = 1203° A 


1100°^ = 1400° A 

1400°-!- = 1700° A 
















Silicon . . 
Diamond . 





In these figures one may find traces of many properties associated 
with firmness of structure or intensity of self-affinity. For example, 
the order of sequence of the energy-quotients agrees essentially with 
that of tenacity and of hardness. There is some relationship also to 
boiling points and melting-points, although here there are more ex- 
ceptions. " Chemical affinity " is so much affected by electrical relations 
and by atomic volume that one would expect to find regularity only on 
comparing similar elements. Such comparison (zinc with cadmium, or 
carbon with silicon) seems to show that the energy-quotient tends to 
increase with diminishing atomic weight. 

Having thus plausible inference, from independent sources, as to the 
relative values of the compressing agencies existing in metals at the 
ordinary temperature, it is worth while to study the correction which 
must be applied to the volume-change exhibited in chemical combina- 
tion with another element. In zinc the self-affinity is so great (boiling 
point = 1200° A), and the metal is hence already so compressed, that 
a given further pressure causes less change in its volume than it would 
cause in the case of mercury. That is, the mercury contracts more 
than zinc when it is oxidized. Hence the difference between the 
volume of the oxide and the volume of the metal gives too low a 
value for the volume of the combined oxygen in the case of mercury. 


Thus the contraction of the oxygen is really less in the case of 
mercuric oxide, although it appears to be the same. 

Without going further, one can explain by means of these considera- 
tions the behavior of zincic and mercuric oxides when subjected to high 
temperatures. The sixteen grams of oxygen in mercuric oxide occupies 
a larger space than an equal weight in the case of zinc, hence one 
infers that it is less compressed by its affinity, hence the affinity must be 
less. This smaller affinity should be more easily overcome by rising 
temperature, a prediction which agrees with facts. Thus there appears 
to be in this case a connection between the compression of substances 
and their tendency to combine one with another. 

The case under consideration is typical. In the case of sodium and 
magnesium, the affinity of the metal for oxygen is so enormous as to 
overcome easily the large affinity of the metal for itself, and besides this 
to compress both metal and oxygen together into a space smaller than 
that previously occupied by the metal. This fact corresponds with the 
great difficulty of decomposing sodic and magnesic oxides. Metallic 
magnesium probably has as energy-quotient a stress more than four times 
as great as sodium (see table on p. 10) ; hence the total contraction on 
combination with oxygen is less than in the case of sodium. Compari- 
son with the cases of mercury and zinc will show that this small con- 
traction does not necessarily conflict with the fact that magnesium 
decomposes sodic oxide at high temperatures. Again, the contraction 
involved in the formation of argentic oxide is very slight. In this case 
the large volume of oxygen is not concealed by the contraction of the 
metallic element, as it was in the case of mercury, for silver is not par- 
ticularly compressible. Hence one can infer that the affinity of silver for 
oxygen is smaller than that of magnesium for oxygen, — an inference 
which agrees with fact. Moreover, since the relation is nearly additive, 
that is, neither silver nor oxygen change much in volume on com- 
bination, their combination is easily shifted, that is to say, silver oxide 
is easily decomposed by heat. 

Of course many tables comparing the molecular volumes of solids and 
liquids might be drawn up, since a very great number of specific gravi- 
ties have been determined. A table containing chlorides of the metals 
already considered may be of interest. 

Here the variations in contraction are less than they were before. 
Chlorine evidently possesses more equally distributed affinities than 
oxygen does, and apparently somewhat weaker ones. The two most 
interesting features of this table, which may be seen without the eliini- 


Molecular Volumes of Chlorides. 


Weight of 
metal com- 
bined with 
35.5 grams 
of chlorine. 





Volume of 

given weight 

of metal. 

Volume of 


weight of 



of volume 

of chloride 

above metal. 

Ag . . 










14.00 . 












|Cu . 








iCo . . 








iCd . 








i Zn . 








Mg. . 








Na . . 

. . 






+ 4.2 

K. . . 







- 8.4 

Rb . . 







- 1.0 

II . . 

• • 




14.1 (?) 



Combined with ca 
Liquid chlorine at 


-80° (boili 

ng point, 1 

60 mm.) (s] 

a. gr. = 1.66 


+80° (sp. | 

;r. = 1.20 ; 


nation of the self-affinities of the several metals, are the small excess in 
the case of silver, and the larger excess in the case of mercurous chloride. 
This is quite in accord with the facts; for argentic chloride is more 
stable than the oxide, and mercurous chloride easily splits into mercuric 
chloride and mercury.* 

The case of the hydroxides is especially interesting. 

The density of the hydroxide of zinc has not been accurately deter- 
mined ; indeed the data concerning cobalt, cadmium, and magnesium are 
not very trustworthy on account of the amorphous condition of most hy- 
droxides. It is interesting to note that in this table, where the substances 
are arranged in the order of the contraction which ensues when hydroxyl 
combines with the metal, should also be arranged in the electro-chemical 

* Richards, These Proceedings, 33, 9 (1897). 


Molecular Volumes or Hydroxides. 


Weight of 
metal com- 
bined with 
17 grams 






Volume of 

given weight 

of metal. 

Volume of 



Excess of 

volume of 


above metal. 


1 Hg . . . 
\ Cu . . . 

Tlie hydroxide is exceedingly unstable. 

It is doubtful if the hydroxide exists. 

The hydroxide cannot be dried without decomposition. 

\ Co . . . 
\ Cd . . . 
\ Mg . . . 
\ Sr ... 
Na . . . . 
























+ 9.51 
+ 8.78 
+ 5.90 
- 0.3 
- 4.9 

Hvdroxvl i" nrcranin nomnoiinds 

+12 ( 



droxyl in I13 

'drogen di 

oxide (sp. 

gr. = 1.50) . . 11.4 


order. That is to say, the solution tension of a metal appears to be 
associated with the excess of affinity of the metal for hydroxyl over its 
affinity for itself, and intensity of potential seems to be associated with 
intensity of atomic compression. The inference to be drawn from this 
comparison is of course that the formation of the metallic ion in water is 
connected with the affinity of the metal for water, — an affinity 
which manifests itself even when both of the " bonds" of oxygen are 
filled.* Similar attraction for nitrogen or sulphur would explain cases 
in which the solvent does not contain oxygen. 

If this is true, contraction should take place when salts are dissolved 
in water. This inference is amply verified by facts. In some cases the 
solution occupies even less space than the water alone, involving a total 
contraction greater than the volume of the salt itself. The best known 
of these cases are those of lithic, sodic, and baric hydroxides, and 

* Briihl has suggested that oxygen is the cause of dissociation, but he ascribes 
it rather to quadrivalence than to a general affinity. 


cobalt, nickel, zinc, and magnesium sulphates,* but undoubtedly others 
exist. In a large majority of cases when an electrolyte is dissolved in 
water, the sum of the volumes of salt and of the solvent taken together 
considerably exceeds the volume of the solution. This contraction is 
usually ascribed wholly to the dissolved substance in dilute solutions,! 
but it seems to me that the behavior of the salts named above proves the 
falsity of this method of calculation. The water as well as the salt must 
contract ivhen a salt is dissolved. So many complications are concerned 
in the act of the solution of an electrolyte that it is difficult to unravel 
the tangled clues ; but the wide deviations exhibited by different sub- 
stances seem to indicate that there are present overlapping contractions 
and expansions, the resultant of which is a smaller quantity than some 
of the individual influences. Such contractions and expansions are just 
what one would expect to find in a readjustment of affinities. 

In considering the simpler case of solid non-electrolytes, one usually 
finds here also a contraction upon solution, although less marked than in 
the extreme cases named above. For this reason, one is inclined to 
ascribe the act of solution of all kinds primarily to the affinity of the 
solvent for the dissolved substance. The solution tension of a metal or 
salt becomes simply a balance or ratio of attractions, — the sejiarating 
tendency of heat upon the dissolving phase is much assisted by the 
attraction from outside. This is of course no new idea. The possible 
method of treating mathematically these balanced influences is suggested 
in a recent paper on the "driving tendency" of reaction. $ 

That electrolytic separation also should be assisted by the outside 
attraction for the solvent is almost a foregone conclusion. This may be 
inferred from the contraction shown by most electrolytes on dissolving. 
Hence may arise the various contact-potentials exhibited by the same 
substance in different solvents ; for different solvents must possess differ- 
ent affinities. Hence also one would expect to find a much greater 
potential needed for the dissociation of gases than for that of dissolved 

The mechanism of electrolytic dissociation in gases is now usually 

* Thonisen, Thermoehemische Untersuchungen, I. 45 (1882). MacGregor, 
Trans. Roy. Soc. Canada, 1890, p. 19; 1891, p. 15; Trans. Nova Scotia Inst. Nat. 
Sc, 7, 368 (1890). 

t Van't Hoff, Vorlesung. phys. theoret. Cliem., III. p. 41 (1900). Drude and 
Nernst (Z. phys. Cliem., 15, 79 (1896)) ascribe this contraction to "Electro- 

t Richards, Jour. Phys. Chem., 4, 385 (1900). See specially p. 391. 


explained by the aid of the ingenious hypothesis of "electrons," as 
amplified by J. J. Thomson and his students in the brilliant experimental 
researches published in the recent volumes of the Philosophical Magazine. 
This daring hypothesis must not be accepted without reservation, how- 
ever. Some physical objections to it have been suggested by Ernest 
Merritt in his interesting address to the American Association for the 
Advancement of Science ; * and other objections arise when one tries 
with its aid to unravel the tangle of influences involved in purely 
chemical action. The rejected alternative of imagining the atom as 
indivisible, but as capable of receiving widely varying electric charges 
under widely different conditions, has some advantages which the opposite 
hypothesis does not possess. The subject is much too large for discus- 
sion here, however. One phase of it, which bears directly upon the sub- 
ject of the present paper, may receive brief notice. 

The results of Thomson, Townsend, Zeleny f and others seem to indi- 
cate that the bearer of the negative electricity not only carries the high 
charge referred to above, but that it is very small, while the bearer of the 
positive electricity is very large. May it not be the atom itself which thus 
expands and contracts ? This agrees with the verdict of the results of 
atomic compression given above. Change of atomic volume seems to be 
associated with electric stress. This assignment of electric expansibility 
to the atomic sphere of influence might explain other phenomena con- 
cerning the behavior of electrified gases, for example, the increase of 
pressure which is observed when a gas is highly charged.^ Again, the 
great conductivity of a gas with adequate potential and quantity of 
electrical discharge § seems to indicate that then the situation must 
resemble that in a metal, where the spheres of stress fill the whole 
volume occupied by the substance. The temperature must be so high 
under these circumstances that the gas is probably in a condition of 
thermal dissociation. Hence one is inclined to refer the great conduc- 
tivity to the electrical susceptibility of evenly compressed or undistorted 
atoms. The fact that pure metals conduct electricity better than alloys or 
compounds seems to support this conclusion. The permeability of solids 
to cathode rays might be explained by supposing that the smallest particles 
of both solid and gas are much contracted by the negative charge. 

* Proc. Am. As. Adv. Soc, 1900, p. 49. 

t Phil. Mag. [5] 46, 120, (1898). See also Am. Chem. Journ., 25, 340 (1901), 
for a resume' of this work. 

X De la Rue and Miiller, Phil. Trans., 1880, SG. 

§ Trowbridge and Richards, Phil. Mag. [5] 43, 349 (1897). 


It is with some diffidence that this paper attempts to reconcile the facts 
with any hypothesis, for hypotheses sometimes lead to dangerous delu- 
sions. If, however, one never forgets the essential difference between 
fact and hypothetical inference, a theory may afford useful suggestions 
for further research. The facts under discussion in the present paper 
seem to me to be adequately connected by none of the current concep- 
tions concerning atoms, hence it has seemed not wholly pointless to 
postulate a theory which might serve better. The essential elements of 
this theory must be evident from the trend of the hypothetical discussion 
above ; they are not wholly new. Since changes of atomic volume seem 
to be so closely associated with the most intimate properties of substance, 
it seems necessary to assign more importance to the atomic " sphere of 
influence " or the " free space " around the atomic centres than is cus- 
tomary. Indeed, the properties of material seem to be as much concerned 
with the " atomic shell " as with the " atomic centre." The two hypothet- 
ical conceptions are so closely related as to be inseparable. 

Such a point of view leads to the conception of an atom as a compres- 
sible field of force possessing two attractive attributes, chemical affinity 
and gravitation, both of which may be concerned in chemical action. 
Mass may be supposed to be causally connected with gravitation. The 
fact that in many cases affinity diminishes with increasing atomic weight,* 
taken together with the Laws of Faraday and of Dulong and Petit, 
suggests that the two attractive forces in the atom may bear some 
sort of reciprocal or additive relationship to one another, — that the 
product or sum of the two may afford a constant basis for the vibrations 
of heat and electricity. This relation is often hidden by electrical attrac- 
tion, which plays so important a role in chemical action that it is some- 
times hard to distinguish the intensity of chemical affinity proper. In 
such an atom one can imagine that either thermal or electrical vibration 
might cause distention. The phenomena of electricity suggest that 
electricity plays around the atomic surface, while heat seems to be 
concerned with a more fundamental or central agitation. Light-vibra- 
tion, which seems also to be intimately concerned with atomic structure, 
would be assumed to be a surface effect like electrical vibration. 

Such an atom would be compressible under the influence of its own 
affinities as well as under the influence of external pressure. Permanent 

* Van't Hoff, Vorl. th. phys. Chem., III. 87 (1900). Compare also the relation 
of the energy-quotients of similar metals referred to on p. 10 of the present 


atomic distortion would accompany chemical union, and the heat of the 
reaction would be the outcome of the resulting decrease of internal 
energy. Atomic volume and atomic compressibility might limit the 
possibility of distortion ; hence would arise a possible explanation for 
quantivalence, stereochemistry, and crystal form. Many other proper- 
ties of material, too numerous to mention, seem to be explicable in a 
similar way. 

It would be unreasonable to expect the hypothesis thus briefly de- 
scribed to correspond to all known facts. No hypothesis has ever been 
proposed which is wholly satisfactory ; our knowledge is incommensurate 
with the possibilities involved. If, however, a given theory is found to 
explain some relationships better than other hypotheses, it may be of 
service in suggesting new experimental research. Such a service is of 
course the best one which a hypothesis can perform. 

The idea discussed above has been already applied in plausible fashion 
to a wide range of chemical and physical phenomena. If future experi- 
mentation to be carried on here seems to warrant it, these applications 
may form the subject of another communication. 

The object of the present paper may be summed up in a few words, as 
follows : It is pointed out that changing atomic volume may be used as 
an approximate measure of the pressure which causes it, and therefore 
of the affinity which causes the pressure. Some of the difficulties in 
the way of exact interpretation are pointed out, and hints are given 
as to possible modes of overcoming the difficulties. 

The chief outcome of the paper is the following postulate : The atomic 
volume is not constant, but a function of pressure and temperature, and 
probably of electric stress. 

In this connection it is pointed out that chemical affinity is possibly a 
reciprocal function of mass. 

To explain these and many other facts, a modification of the atomic 
hypothesis is tentatively proposed which contends that we have no right 
to disregard the compressible environments around the centres of gravity 
and affinity. 

Cambridge, Mass. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 2. — June, 1901. 



By Roland Thaxter. 



By Roland Thaxter. 

Received May 6, 1901. Presented May 8, 1901. 

Additional material illustrating the well-marked generic type de- 
scribed in a former paper as Mbnoicomyces renders necessary some 
modification of the original diagnosis, as well as the separation of several 
species in a second nearly allied genus, which I have called Eumonoico- 
myces (E. Papuamis being taken as the type), that is well characterized 
not only by constant differences in the structure of the peculiar anther- 
idium, but also by reason of certain differences in gross habit which are 
constant in normal forms of all three of the known species, one of which, 
E. invisibilis, was formerly placed by me in Mbnoicomyces. 


Receptacle consisting of a basal and subbasal cell ; the latter producing 
terminally a sterile appendage and laterally a fertile branch (abnormally 
more than one) the axis of which is coincident with that of the receptacle 
from which it is not distinguished and consists of a series of superposed 
cells which may bear a sterile appendage, an antheridium, or an anther- 
idium and a perithecium ; the three terminal cells usually bearing these 
organs in the order mentioned. The antheridia consisting of a single 
stalk-cell, and a single, often obscure, basal cell; the body of the antherid- 
ium consisting of a series of numerous antheridial cells in four (?) vertical 
rows which extend obliquely inward and upward, emptying into a com- 
mon cavity, and replace entirely the two tiers of wall-cells and the anther- 
idia of Monoicomyces ; the terminal cells growing upward directly to 
form four unequal sterile terminal appendages, similar to those of 


Eumonoicomyces Papuanus nov. sp. 

Nearly or quite hyaline. Basal cell of the receptacle small, usually 
triangular ; the subbasal cell terminating in a short appendage distin- 
guished by a dark basal septum, and sometimes once branched. The 
fertile branch not differentiated from the receptacle, consisting of three, 
rarely two cells similar to the subbasal cell, obliquely superposed; the 
lowest bearing normally a short, hyaline or faintly brownish, erect, sterile 
appendage, similar to that of the subbasal cell ; the middle cell bearing a 
single antheridium, and the upper an antheridium and a stalked perithe- 
cium. The autheridia rather stout, broader distally ; the stalk-cell small 
and short; the antheridial cells very numerous — thirteen to fifteen 
usually visible in optical section — the terminal appendages of the usual 
type, short or seldom longer than the antheridium. Perithecium rather 
long and sometimes slender ; the venter inflated ; the distal portion 
tapering gradually and symmetrically to the blunt, nearly truncate apex ; 
the rather short tip hardly distinguished above a slight elevation ; the 
stalk-cell variable in length, rather slender, seldom more than half as 
long as the perithecium ; the basal cells rather large and broad, not dis- 
tinguished from the venter. Spores about 35 X 3/x. Perithecia 80- 
120 X 32-40^, the stalk-cell 35-75 x 15^. Antheridia including 
stalk-cell and without appendages 35 X 18 fi. Total length to tip of 
perithecium 150-290^. 

On all parts of a small pale species of Oxytelus. Ralum, New Pome- 
rania. Berlin Museum, No. 1011. 

Eumonoicomyces Californicus nov. sp. 

Resembling E. Papuanus in general habit. Basal cell of the recep- 
tacle short, stout, geniculate, with a dark brown suffusion extending from 
the foot half-way up its convex margin ; the subbasal cell bearing distally 
a long appendage consisting of a short hyaline basal cell, separated by a 
dark septum from a second cell above it, which is dark brown and bears 
two long, slender, one-celled, erect branches, brown below, becoming 
hyaline distally. The fertile branch not distinguished from the receptacle 
and consisting of three, sometimes more, very obliquely superposed cells 
similar to the subbasal cell : the lowest bearing a sterile appendage like 
that which terminates the receptacle; the middle cell usually bearing an 
antheridium, and the npper an antheridium and a perithecium. Anther- 
idium short-stalked, with a more or less well-defined median constriction, 
resulting from an inflation of the cells which bear the terminal append- 


ages. The latter very long, brown, extending beyond the tip of the 
peritheciura. Perithecium short and stout, the venter inflated, the much 
shorter neck-like distal portion abruptly distinguished, the apex blunt, 
the stalk-cell usually rather short and stout. Perithecia 75 X 25 ix, the 
stalk-cell 20 X 18 fx. Sterile appendages, longest 150 ^u. Appendages of 
antheridium 100^. Total length to tip of perithecium 150 p. 
On Oxylelus sp. Berkeley, California. 


The characters which may be considered to separate this genus from 
Eumonoicomyces are as follows : — The stalk of the antheridium consists 
of two cells placed side by side ; the body of the antheridium consists of 
two tiers of wall-cells, from each of which an inner antheridial cell is 
separated ; the subbasal cell of the receptacle bears normally more than 
one heterogeneous fertile branch. 

o ■ 

Monoicomyces Echidnoglossae nov. sp. 

Subbasal cell of the receptacle somewhat smaller than the basal cell, 
bearing a terminal appendage the basal cell of which is as long, or nearly 
as long as the receptacle and often distally enlarged ; the axis above it 
consisting of a curved series of several cells, externally opaque, black, 
hyaline along the inner margin, each cell giving rise from its inner side 
to a hyaline simple branchlet, much as in the appendage of Laboulbenia 
cristata. Fertile branches usually two, sometimes one or three, arising 
from the subbasal cell of the receptacle, and consisting of a single short 
basal cell which bears directly a perithecium (in some cases more than 
one) and an antheridium. Antheridium relatively large, the stalk-cells 
somewhat longer and narrower than the basal cells ; the cells of each of 
the middle tiers distally more or less prominent, the rounded, almost 
papillate elevations thus formed from the upper tier more prominent than 
those from the lower tier : the distal cells proliferous externally and dis- 
tally, thus forming an outer crown of shorter appendages of very unequal 
length, which surround the usual inner series. Perithecium becoming 
greatly and asymmetrically inflated below, and tapering rather abruptly 
to the slightly distinguished, rather short, bluntly pointed tip ; the stalk- 
cell variably developed. Perithecia 100-125 X 45-55^, the stalk- 
cells 40-80 x 15 ft. Antheridia 75-100 /j, the sterile appendages 
50-75 li. Total length to tip of perithecium 220-250 fx. 

On the inferior surface of the thorax of Echidnoglossa Americana Fau- 
vel. Vera Pass, Colorado. Leconte Collection. 


Monoicomyces furcillatus nov. sp. 

Receptacle consisting of two small cells which are hardly distinguish- 
able owing to a general blackish brown suffusion ; producing on either 
side a stout blackened prolongation, the two forming a nearly symmetri- 
cal fork-like structure, the prongs of which are slightly curved inward, 
and slightly divergent. From near the base of these outgrowths and 
between them arise, apparently from single basal cells on both sides, 
single stalked perithecia and antheridia. The antheridia rather long 
and slender, their detailed structure not determinable in the types. The 
perithecia long and slender, straight, symmetrical, pale yellowish, slightly 
inflated toward the base, tapering gradually to the blunt apex. Spores 
about 40 X 3 ^. Perithecia 135 X 27^. Outgrowths from the recep- 
tacle 110 X 12 fi. 

Near the tip of the abdomen of Aleochara repetita Sharp. Panama. 
Sharp Collection, No. 1095. Of the three individuals obtained one only 
is in fair condition, and none have antheridia in which the details of 
structure can be made out. Owing to the suffusion and great reduction 
of the receptacle it is further impossible to determine the exact origin of 
the remarkable fork-like outgrowths, or the other structures which arise 
from it. The form is a most peculiar one and recognizable without diffi- 
culty ; yet, until further data are obtained concerning it, its generic 
position cannot be certainly determined, although it seems at least more 
closely allied to Monoicomyces, in which it is provisionally placed, than 
to any other known type. 

Monoicomyces Aleocharae nov. sp. 
Pale amber, shading to amber brown. Receptacle, together with the 
foot and the basal cell of the terminal appendage, forming a heart-shaped 
body, blackened below, bearing terminally a median, rigid, slender, almost 
wholly opaque, black branch, abruptly distinguished from its broad basal 
cell : the subbasal cell of the receptacle small, triangular when viewed 
side wise, giving rise to two fertile branches, the short small basal cells 
of which give rise at once each to two secondary branches and an anther- 
idium ; the branchlets proliferous and forming an axis of usually three 
cells, the lower bearing an antheridium, and each of the two upper an 
antheridium and a perithecium ; there being thus sixteen antheridia and 
eight perithecia, in fully and symmetrically developed specimens, which 
form a dense, spreading, fan-like tuft, the antheridia being in general 
posterior in position, overlapping one another between the black sterile 


appendage and the perithecia. Antheridium distally broadened and 
truncate, elongate ; the stalk-cells about equal and about one half the 
length of the body of the antheridium or somewhat longer than this ; the 
basal cells unequal ; the cells of the two middle tiers, and their antheridia, 
clearly distinguishable ; the terminal cells forming four unequal, rounded 
prominences, the upper inner angle of each cell separated by an almost 
vertical septum to form the four " guard cells," that terminate in papillate 
prominences just below which they proliferate to form the characteristic, 
erect, sterile appendages, all four of which do not always develop; the 
sterile appendages relatively short, two to three-septate, tapering to a 
blunt point, distinctly inflated above the slightly constricted base. Peri- 
thecium relatively large, straight or slightly curved, somewhat inflated 
below, tapering gradually to the rather short, moderately well distin- 
guished tip ; the apex bluntly rounded, the basal cells relatively small ; 
the stalk-cell variably developed, its distal end usually somewhat broader 
than the basal cells collectively, sometimes more than half as long as the 
body of the perithecium. Spores about 50-55 X 4-5 ft. Perithecia 
130-185 x 35-55 ^ the stalk-cell 35-100 X 18-25^. Antheridia 70- 
75 x 22 /j, its appendages 45-50 p. Receptacle about 35 x 28 p. 
Greatest general length and width of largest individual 350 X 300 ^. 

On Aleochara rujipes Boh. Derema, Usambara, East Africa. Berlin 
Museum, Nos. 844 and 845. 


Receptacle consisting of two cells, the upper bearing a free stalked 
antheridium and a stalked perithecium. Antheridium conical, consisting 
of a single stalk-cell followed by a basal cell from which is separated 
a group of smaller cells some of which (two or four ?) extend upward 
and inward to form antheridial cells : above these follow three external 
marginal cells, the lowest of which lies beside the antheridial cells; the 
uppermost succeeded by a conical chamber terminating in a pore, and 
extending downward along the inner sides of the marginal cells to form 
a cavity into which the antheridial cells empty. Perithecium resembling 
that of Haplomyces and having two ascogenic cells. 

Euhaplomyces Ancyrophori nov. sp. 

Receptacle small, the basal cell somewhat longer, nearly hyaline, 
tapering to the relatively small foot; the subbasal cell becoming pale 
amber brown. Antheridium, including its short stalk-cell, about as long 


as the receptacle, becoming pale amber brown, tapering to a pointed 
apex. Perithecium becoming pale amber brown, relatively large, thick 
walled, considerably and abruptly inflated above the basal cells, somewhat 
asymmetrical, tapering rather evenly to the blunt apex; the stalk-cell 
long, thick walled, slightly curved, nearly hyaline, distally somewhat 
broader, not distinguished from the basal cells. Spores about 40-45 
X 3.5 fi. Perithecia 180-200 X 72-82 /* ; the stalk-cell 110-120 X 
28-30 /a. Antheridium including the stalk-cell 55-65 /x. Total length 
to tip of perithecium 360 fi. 

On the superior surface of the abdomen of Aneyrophorus aureus. 
Dumfriesshire, Scotland. Sharp Collection, No. 1091. 

Eucantharomyces Xanthophaeae nov. sp. 

Perithecium (not fully mature) straw colored, somewhat asymmetrical, 
almost symmetrically and but slightly inflated from base to apex; the 
tip short, well distinguished ; the lip-cells rounded, and slightly inflated, 
forming a knob-like termination, one of them protruding in the form of 
a slight tongue-like projection beyond the others : the stalk-cell about 
as long as the receptacle, from which it projects at an angle, being more- 
over turned at the same time a little to one side. The cells of the recep- 
tacle subequal, lying side by side, the basal one extending to the base of 
the stalk-cell of the perithecium, with which it is in contact. Appendage 
relatively large, the stalk-cell subtriangular, somewhat larger than the 
basal cell which is wholly overlapped externally by the well defined and 
distally somewhat inflated marginal cell; the antheridial cells in four 
tiers of seven, six, five and four cells respectively; the discharge-tube 
long and curved outward. Spores about 36 x4ju. Perithecia 165 X 
50 fj., the stalk-cell 46 X 20 p. The appendage to tip of discharge tube 
120 fj., the antheridium proper 55 X 30 /x. Total length to tip of peri- 
thecium 290 fx. 

On the right inferior margin of the prothorax of Xanthophaea vittata 
Dej., Australia. Berlin Museum, No 973. 

Dichomyces bifidus nov. sp. 

Basal cell slightly enlarged, pellucid, tinged with brown, about as long 
as broad : the lower tier, and more or less of the middle tier, opaque ; 
the marginal cells of the latter forming a bluntly rounded, sometimes 
almost obsolete projection on either side, hardly extending above the 


venter of the short, stout, short-necked antheridia : the upper tier 
relatively large, more or less crescent-shaped according to the degree of 
lateral development, edged externally with blackish brown, more broadly 
below, the brown area punctate ; the cells about thirty-one in the larger 
individuals, the marginal ones forming a rather slender series, which 
may curve abruptly upward nearly to the middle of the perithecia, or 
assume a more divergent* habit ; the perithecigerous area horizontal, pro- 
ducing normally four perithecia, three appendages arising between the 
two middle ones and one between each of the others, the external cells 
bearing appendages as usual which vary in length. Perithecia rather 
long and slender, hyaline or faintly yellowish brown, conspicuously 
tinged with purplish brown below the perfectly hyaline tip, the anterior 
lip-cells forming a pointed projection, the posterior ones forming each a 
relatively large ear-like appendage which tapers to a pointed apex, and 
is slightly curved, the two diverging from one another at an angle of 
about 50°. Spores about 38 X 2.5 fx. Perithecium without appendages 
126 X 25/x.; the appendages 14^. Receptacle 220-350 X 120-165 /a. 
Total length to tip of perithecium 300-330 /x. Appendages 20-80 fx. 

Ou the abdomen of (?) Philonthus sp. Ralum, New Pomerauia. 
Berlin Museum, No. 1013. 

Dichomyces Belonuchi nov. sp. 

Receptacle relatively large and long : the distal tier relatively small, 
consisting of from eleven to thirteen short cells, slightly suffused, the 
median cells little longer than the rest, the series forming slight, rounded, 
sometimes almost obsolete lateral projections on either side of the peri- 
thecia : the basal cell small, partly transparent : the lower and middle 
tiers not distinguished, uniformly opaque • a portion of the middle cell, 
and sometimes the tips of other cells in the middle tier, more or less 
translucent, the marginal cells ending in a slight rounded prominence 
below the base of the antheridium. Perithecia normally two, evenly 
suffused with pale reddish brown, rather long and slender, tapering 
throughout, the conformation of the lip-cells much as in D. furciferus. 
Spores about 30 X 3 ll. Perithecia 75-80 X 18-20 /x. Receptacle 
108-126 X 54-58,1/. Total length to tips of perithecia 185-200 /x. 

On the abdomen of Belonuchus fuscipes Fauvel. New Guinea. 
Sharp collection, No. 1090. 


Dichomyces Australiensis nov. sp. 

Receptacle usually rather loug and narrow, the basal cell relatively 
large, hyaline or slightly suffused; the margins of the lower tier usually 
continuous with those of the middle one, the marginal cells deep blackish 
brown or quite opaque, the middle cell hyaline or translucent throughout, 
its lower third often punctate : the middle tier consisting of about nine 
cells, slightly suffused with pale reddish brown externally, more or less 
edged with deep blackish brown; the terminal cells forming a free 
rounded projection on either side, extending as high as about the middle 
of the rather large antheridia, the tips of which may reach to the bases 
of the perithecia : the upper tier nearly hyaline, consisting normally of 
from eleven to thirteen subequal cells, the terminal ones extending but 
slightly higher than the bases of the perithecia, which are normally two 
in number, rather deeply suffused with purplish brown throughout ; the 
apex hyaline, the posterior lip-cells producing each a relatively large 
bluntly pointed appendage, the two diverging nearly at right angles to 
the axis of the perithecium, becoming slightly recurved, the distance from 
tip to tip about twice the diameter of the perithecium. Appendages 
nearly as long as the perithecia. Perithecium 60-70 X 16-20/*, its 
appendages 18/*. Receptacle 90-100 X 42-48/*. Total length to tip 
of perithecium 160-170 /*. 

On the superior surface of the abdomen of Quedius riificollis Grav. 
Sharp Collection, No. 1102. 

Dichomyces Mexicanus nov. sp. 
General habit much like that of D. prhiceps, generally rather long and 
slender. Basal cell hyaline, the lower tier relatively long and narrow, 
broadly edged externally with black ; the median cell hyaline, or only the 
marginal cells slightly suffused with smoky brown : the middle tier dis- 
tinguished from the lower by a slight prominence, hyaline, seven to nine 
celled; the marginal cells protruding but slightly on either side; the 
antheridia brownish, short, stout, blunt pointed : the upper tier relatively 
very long, sometimes twice as long as the middle tier, consisting of from 
nine to eleven cells ; the marginal cells protruding but slightly on either 
side, very much as in the middle tier. Perithecia normally two, about 
as long as the distal tier and concolorous with it, or somewhat darker, 
rather stout, tapering but slightly; the tip rather abruptly distinguished, 
broadly truncate with a slight median projection ; the posterior lip-cells 
giving rise each to a long horizontal appendage, which becomes recurved, 


is bluntly pointed and somewhat narrower toward the base, the distance 
from tip to tip often twice the diameter of the perithecium. In a few 
specimens the receptacle and perithecia are somewhat evenly suffused 
with smoky brown. Perithecia 75-85 X 25-30 jx, the appendages 18- 
22 ix. Receptacle 165-200 X 55-70 /x. Total length 235-275 fx. 

On the inferior surface of the abdomen of Philonthus atriceps Sharp. 
Jalapa, Mexico. Sharp Collection, No. 1112. Specimens, apparently 
normal, sometimes occur in which the tips of the perithecia are blunt 
and unmodified. 

Dichomyces Homalotae nov. sp. 

Form short and stout. Basal cell geniculate, more or less suffused : 
the lower tier more or less, sometimes wholly, suffused with reddish 
brown ; the margins darker, more or less translucent, without contrasts, 
the outline somewhat uneven, the transition to the middle tier indicated 
by a distinct prominence: the middle tier consisting of from nine to 
(rarely) thirteen cells, hyaline or subhyaline, with slight lateral suf- 
fusions ; the marginal cells ending in a slight hyaline rounded projection, 
seldom extending higher than the venter of the somewhat suffused 
curved antheridia : the upper tier relatively small, the cells subequal, 
hyaline, asymmetrical, owing to the development of but one perithecium ; 
the appendages often equalling, or exceeding the perithecium in length. 
Perithecium characteristically short and stout, inflated below, sometimes 
oval, tapering somewhat abruptly distally, to the rather broadly truncate, 
or slightly rounded unmodified apex. Spores 33 X 3 /x. Perithecia 
65-75 X 25-30 /a. Receptacle 70-90 X 40-55/1. Total length 125- 
165 fx. 

On all parts of Homalota sordida Marsh. Fresh Pond, Cambridge. 
First observed by Mr. Bullard. 

Peyritschiella Xanthopygi nov. sp. 

Basal cell of the receptacle very small, or hardly distinguished from the 
foot : the first tier consisting of three subequal cells without appendages, 
the middle one somewhat shorter than those on either side of it : the 
second tier asymmetrical, consisting of three subequal median cells, the 
margins of the two outer free below for nearly half their length and 
coincident with the margins of the tier below, the appendiculate " margi- 
nal " cells, about three to five on either side, separated from them as 
usual by oblique septa ; the first on the right bearing the large, slender, 
pointed, nearly straight purplish antheridium : the upper tier consisting 


of about fifteen or more cells, the series distally concave, rising abruptly 
upward on either side above the base of the perithecium and bearing the 
usual appendages. Perithecium solitary at the right of the median 
(primary) appendage, almost symmetrically inflated from base to apex, 
dull purplish ; the tip slightly darker, hardly distinguished ; the apex 
truncate, sometimes slightly spreading; the lip-cells hardly projecting. 
Perithecia 115-150x34-42^. Receptacle 200 X 65-70 p. Total 
length to tip of perithecium 310-360 /x. 

On the abdomen of Xanthopyyus Solskyi Sharp. Sharp Collection, No. 
1158. Nearly allied to P. Amazonica, from which it differs principally 
in the form of the perithecium. 

Chitonomyces occultus nov. sp. 

Short and stout, becoming suffused with somewhat smoky amber 
brown. Lower portion of the receptacle deeper brown, the basal cell 
relatively large, broad distally ; the subbasal cell broad and flattened ; 
the lower cell of the distal portion rather large and but slightly over- 
lapped by the subterminal cell, which may bulge slightly below the 
terminal cell, the latter being thus turned so as slightly to overlap the 
perithecium. Perithecium short and stout, its upper third or less free, 
darker brownish externally ; the tip bent outward, tapering rather 
abruptly to the slightly irregular apex, its outer half or less suffused 
with dark brown. Spores about 22 X 2.5 xi. Perithecium 60 X 20 xi. 
Receptacle to tip of distal cell 90 /x. Total length to tip of perithecium 

100 ft. 

In the median marginal depression of the right elytron of Onemidotus 
sp. Lake Eustis, Florida. 

Chitonomyces psittacopsis nov. sp. 

Nearly hyaline. Receptacle rather slender, the basal cell several times 
as long as the squarish subbasal cell ; the cell above the latter nearly 
equalling it in size and separated by an oblique septum from the lowest 
of the marginal cells, which are all subequal ; the terminal appendiculate 
cell of the usual form, relatively large and long, without any distinct 
basal enlargement; the tip of the lower appendiculate cell curved slightly 
outward. Perithecium relatively very large, long, slender, usually 
curved sidewise throughout, the upper half tapering very slightly to the 
curiously modified, clear black contrasting tip, which resembles the 
partly open beak of a parrot ; a larger upper recurved mandible-like pro- 


cess being separated from a second, that resembles a lower mandible, 
by a hyaline area which includes, and extends back from, the pore ; the 
lower lip-cells translucent, but suffused with brown in such a way as to 
suggest a tongue-like process projecting slightly between the " mandi- 
bles." Spores very numerous, completely filling the cavity of the 
perithecium, greatly attenuated, 85 X 2.5 /a. Perithecium 200 X 30 jx. 
Receptacle to tip of distal cell 140 /a. Total length to tip of perithe- 
cium 290-300 fi. 

On the posterior legs of Laccophilus sp. Lake Eustis, Florida. 

Chitonomyces Bullardi nov. sp. 

Straw colored becoming tinged with pale amber brown. Basal cell of 
the receptacle monstrously developed, about as long, sometimes twice as 
long, as the remainder of the plant, its axis coincident with that of a distal, 
variably developed, blunt, tooth-like, free posterior projection, near the 
base of which the subbasal cell and the remainder of the plant project 
backward at an angle of about 45° , or less, to the axis of the basal cell, 
the separating septum being vertical or nearly so ; the subbasal cell small 
and flattened : the lower marginal cell of the distal portion of the recep- 
tacle subtriangular, short and broad ; the lower appendiculate cell above 
it relatively large ; the subterminal cell larger than the lower marginal 
cell, curved inward so that the terminal appendiculate cell projects from 
it obliquely inward against the perithecium. Perithecium four fifths 
or more free, relatively large and stout, distinctly inflated below, taper- 
ing to the tip, which is characteristically modified through the presence 
of a large claw-like subterminal dark amber brown external projection, 
the distal half of which is somewhat abruptly recurved, like the upper 
mandible of a parrot, over the small hyaline incurved 4-papillate apex, 
which is immediately subtended on the inner side by a small, erect, 
dark amber brown, tooth-like process, the blunt tip of which alone is 
free. Appendages slender and extending to or beyond the tip of the 
perithecium. Spores about 20 X 2.5 /x. Perithecium average 70-75 x 
30-32 ft not including the hook-like appendage, which is 25 /x to its upper 
margin. Receptacle : basal cell to tip of prolongation 90-220 X 15- 
22 fx, the portion above to tip of distal cell 48 /x. 

On the right inferior anterior margin of the prothorax of Cnemidotus 
12-punctatus Say. Glacialis Pond, Cambridge. The most singular 
species of the genus, discovered by Mr. Charles Bullard, to whom I take 
pleasure in dedicating the species. 


Chitonomyces Hydropori nov. sp. 

Receptacle nearly hyaline, the subbasal cell flattened, many times 
smaller than the basal cell, slightly inflated and distinguished from the 
cells above and below by slight constrictions ; the two cells above sub- 
equal, the posterior somewhat broader, and separated from the lower 
marginal cell of the distal portion by an oblique curved septum, which 
overlaps its upper fourth ; the subterminal marginal cell often nearly as 
long as the lower, the narrow upper half or more of which it overlaps. 
The lower appendiculate cell rather small, the upper terminal one of the 
typical form, relatively rather long, distinguished by a slight constriction, 
the appendage extending beyond the tip of the perithecium. Perithecium 
relatively large, its upper half or more free, distally broader, the outer 
margin nearly straight with a slight subterminal rounded elevation below 
the abruptly rounded projecting outer brownish lip-cells ; the apex other- 
wise flat, broad, bent outward so as to be slightly oblique, the inner 
margin below it bulging and curved throughout. Spores 55 X 4/*. 
Perithecium 98-108 X 25 /a. Receptacle to base of perithecium 80 //, to 
tip of terminal cell 150 /a. Total length to tip of perithecium 185 yu,. 

On the mid-elytron of Hydroporus modesties Aube. Cape Neddock, 
Maine. Mr. Bullard. 

Chitonomyces Orectogyri nov. sp. 

Dull purplish, the cells thick walled and marked by faint transverse 
striations. The basal cell of the receptacle very small and hardly dis- 
tinguishable, owing to an abrupt curvature just above the foot ; the sub- 
basal cell relatively large, distally narrowed, nearly the whole upper half 
of its posterior margin covered by a relatively large triangular cell, from 
which it is separated by a nearly vertical septum ; this triangular cell is 
in contact distally with the ascigerous cavity and the base of the lowest 
marginal cell ; the latter is very long, extending upward, its narrow 
extremity ending without enlargement opposite the blackened base of the 
inner appendage, lying between the latter and the tip of the perithecium; 
the lower appendiculate cell well defined, about two thirds as long as the 
subterminal cell, which projects slightly above and bears the free terminal 
appendiculate cell, which is hyaline, about equal to the lower in length, 
its inner margin nearly straight, its outer margin curved abruptly inward 
to the base of the obliquely distinguished, blackened, narrow, erect ter- 
minal portion, from which the appendage has been broken in the types. 
Perithecium relatively large, of nearly equal diameter throughout ; the 


tip broad with a bluntly rounded apex ; a short erect contrasting brown 
prominence formed by the left posterior lip-cell, toward the base of which 
the inner (anterior) lip-cells are curved iu a characteristic fashion, so as 
partly to overlap it. Spores about 75 X 5 \x. Perithecium 125 x oG ft. 
Receptacle 250-270 /*. Total length to tip of perithecium 255 jx. 

On the superior surface of the tip of the abdomen of Orectogyrus 
specular is Aube. Africa. Berlin Museum, No. 606. 

DIOICOMYCES nov. geu. 

Male individual consisting of four superposed cells, the upper of 
which is a simple antheridium bearing a subterrainal discharge tube. 

Female individual. Receptacle ending distally in a peculiarly modi- 
fied sterile cell, corresponding to the upper spore-segment: the subbasal 
cell producing a single perithecium laterally, and separated from the 
sterile terminal cell by a second small cell. Perithecium free, stalked ; 
the ascogenic cell single, the spores more or less obliquely once-septate, 
and of two kinds corresponding to the sexes. 

Dioicomyces Floridanus, formerly referred provisionally to Amor- 
pkomyces, must be transferred to this genus ; since, although the male 
is unknown, the female has the typical characters which distinguish the 
genus very clearly from its near ally. D. obliqueseptatus on Myrmed&nia 
(?) sp. must also be removed from Amorphomyces, on account of its 
obliquely septate spores, and should with little doubt be included in the 
present genus; although it is evident, from comparison with abundant 
material of the species described below, that the specimens, both females, 
from which the original description was made, are more imperfect than 
was at first supposed, and should not have been used as types. The 
peculiar sterile cell is present in neither of these ; but, since they corres- 
pond in all other respects to the generic type, may be assumed to have 
been broken off. No free spores are available in either, although an ex- 
amination of the spore mass within the ascus seems to show that they 
present the same variation in size which characterizes the species described 

Dioicomyces Anthici nov. sp. 

Male individual. Form slender, of nearly the same diameter through- 
out, the basal cell half the total length of the individual to the tip of the 
discharge tube ; the third cell nearly square, the subbasal about as large 
as the terminal antheridial cell, which ends in a distal blunt projection ; 
the discharge-tube arising laterally below the tip, projecting upward from 



a broadened base, slightly divergent from the main axis, slender, about 
as long, or a little longer than, the body of the antheridial cell. Length 
to tip of antheridial cell, including foot, 50 fx : to tip of discharge-tube 
GO^c. Width 8 fi. 

Female individual. Often more or less strongly curved, the terminal 
sterile cell bluntly pointed, slightly curved, brownish ; the basal cell 
becoming narrower below, the upper septum convex ; tinged with brown 
posteriorly as is the rest of the receptacle : the subbasal cell very small, 
subtriangular ; separated from the terminal sterile cell by a somewhat 
smaller triangular cell. Stalk-cell of the perithecium hyaline, long, often 
about the same diameter throughout; the thick wall becoming gradually 
thicker distally : the perithecium slightly inflated, faintly brownish ; the 
short, stout, broad, blunt tip slightly distinguished, and nearly symmetri- 
cal ; the lip-cells forming an unbroken outline, without protrusions. 
Spores (male) 40x4/i, (female) 60 X 6 jx. Perithecium 100-110 X 
35-45 /a, the stalk-cell 75-115 x 18 /x. Receptacle including foot 35 x 
1*2 /a, the sterile terminal cell 18-25 X 7-9 fx. Total length to tip of 
perithecium 185-220 /x. 

On Anthicus fioralis Linu. Fresh Pond, Cambridge. On A. Califor- 
nicus Laf. California (Lecoute Collection). 

Dioicomyces onchophorus nov. sp. 

Male individual similar to that of D. Ant hid, slightly smaller. 

Female individual. Usually strongly curved, especially at the base 
of the stalk-cell ; similar to D. Anthid ; the receptacle, sterile cell, and 
the stalk of the perithecium, relatively smaller. Perithecium dirty 
brown, one of the lip-cells protruding in the form of a well defined, 
lateral, finger-like, erect, straight, or slightly curved, blunt-tipped, cou- 
colorous process ; an irregular anterior elevation or angular prominence 
is also more or less well defined above the middle of the perithecium. 
Spores (male) 35 x 4/x, (female) 45 X 5 /x. Perithecia to tip of pro- 
jection 125-140 X 40-45 fx, the stalk-cell 90 p. Total length to tip of 
perithecium 210-230 fx. 

Usually on the basal half or at the base of the left elytron of Anthicus 
floralis Linn. Fresh Pond, Cambridge. 

Dioicomyces spinigerus nov. sp. 

Male individual similar to that of D. Anthici, much smaller, the ex- 
tremity less prominent, or almost horizontal, the discharge tube some- 


what more slender, and more often erect. Total length including foot 
40 X 6.5 fx; to tip of discharge-tube 47 /x. 

Female individual. Receptacle relatively small, tinged with dirty 
yellowish, edged with brown to the tip of the small terminal sterile cell. 
Perithecium dirty yellowish and relatively large, considerably and more 
or less symmetrically inflated, above and including its basal cells, to the 
base of the tip, which is bent abruptly outward at right angles to the axis 
of the perithecium; the apex broad, blunt, the lip-cells hardly projecting: 
a unicellular brown, straight or slightly curved, spine-like process, which 
tapers to a blunt point, projects upward at an angle of about 45° from 
the middle of the outer (anterior) .margin of the perithecium ; and a 
slight elevation is also more or less distinct between its base and that of 
the tip ; the stalk-cell relatively short, becoming rapidly narrower toward 
its base. Spores (male) 26 X 4 /x, (female) 40 X 6 /x. Perithecia 
including basal cells 125 X 50 fx, the spinous process 55 /x, the stalk-cell 
36-40^. Receptacle to tip of sterile cell about 45 [x. Total length to 
tip of perithecium about 185 fx. 

On Anthicus Jloralis Linn., with the last two species, more commonly 
on the inferior surface of the abdomen. Fresh Pond, Cambridge. 

Teratomyces Zealandica nov. sp. 

Receptacle with a distinct distal obliquity, opaque with the exception 
of a hyaline area just above the foot, the margins straight, the distal por- 
tion relatively narrow, the base relatively broad, the suffusion involving 
the bases of the appendiculate cells which are relatively numerous and 
narrow and more or less suffused with brownish yellow. Appendages 
sometimes scanty, but slightly divergent, concolorous throughout, nearly 
hyaline or pale yellowish ; the basal cells of the larger branches rela- 
tively slender, the external branchlets and numerous beak-like cells hardly 
more deeply colored. Perithecia relatively large, long, rather slender, 
slightly inflated throughout, the blunt tip more or less abruptly distin- 
guished ; the stalk-cell very short or almost obsolete, hidden by the 
appendages; the basal cells relatively small and not distinguished from 
the body of the perithecium. Spores about 50 X 2.5-3 fi. Perithecia 
150-180 X 20-28 fx, basal and stalk-cells together about 35 /x. Longest 
appendage 180 /^. Receptacle 75-125 X 15-18 (base) 22-30 /x (distally). 

On Quedius insolitus Sharp. Dunedin, New Zealand. Sharp Collec- 
tion, No. 1099. 


Teratomyces petiolatus nov. sp. 

Receptacle nearly symmetrical, almost wholly black, slender below, 
expanding rather abruptly distally ; the appendiculate cells relatively 
large and long, translucent, brownish yellow, subtended by a slight en- 
largement. Appendages numerous, spreading, the larger ones consisting 
of a very large colorless or brownish basal cell, which bears a series of 
branchlets externally and several branches terminally ; the branchlets 
usually short, and two-celled, the distal cell usually long, beak-like and 
clear purplish brown, the lower cell hyaline or light brown and in the 
lower branchlets usually bearing long-necked antheridia: the terminal 
branches with several short branchlets of a similar character. The 
smaller shorter appendages ahout the bases of the larger ones, mostly 
dark purplish brown, with many beak-like cells. Perithecia usually 
several, large, symmetrical, purplish brown ; the tip short, rather narrow 
and abruptly distinguished ; the basal cells relatively very large, forming 
a portion of the stalk sometimes half as long as the perithecium proper ; 
the stalk-cell stout and elongate. Perithecia 185-225 X 45-50 /a, the 
basal cell 100-150 x 10//., the stalk-cells 180-300 /*.. Receptacle about 
150 /a. Appendage, longest 175, longest basal cells 110 //.. 

On Quedius sp. Greymouth, New Zealand. Sharp Collection, 
No. 1103. 

Teratomyces insignis nov. sp. 

Receptacle usually quite opaque, long, slender ; the outline unbroken 
and nearly straight, tapering evenly to the slightly geniculate base, which 
is nearly hyaline just above the foot: the margin of the suffused area 
distally strongly oblique, especially before maturity ; the appendiculate 
cells small, becoming brownish. The appendages numerous, spreading, 
the larger ones hyaline or nearly so, consisting of a large elongate basal 
cell, which bears two or ihree small remote antheridial branches exter- 
nally ; and terminally, as a rule, two large branches placed side by side 
(one of which may be wanting) sometimes associated with one or two sub- 
terminal smaller branchlets, the basal cells of which are dark contrasting 
brown : the terminal branches hyaline with branchlets like those of the 
basal cell ; the branchlets, however, more numerous, contrasting, brown, 
simple or branched, many having characteristic beak-like terminations, 
while others are blunt tipped, with oblique septa. The smaller peripheral 
appendages more or less crowded around the bases of the larger ones, 
with conspicuous and numerous beak-like terminations. The antheridia 
with long curved necks. Perithecia usually several, brown, long and 


slender, straight, very slightly inflated near the base, with a slight sub- 
median enlargement ; tapering throughout to the short, truncate, well 
distinguished tip : the basal cells rather small, concolorous ; the group 
narrower than the stalk-cell and separated from it by a horizontal sep- 
tum : the stalk-cell very large, usually elongate, often inflated and thick 
walled. Spores about 50 X 4 jx. Perithecia including basal cells 240- 
275 x 40 ( u, the stalk-cell 150-325 X 25-85 /x. Appendages, longest 
225,0.. Receptacle 100-185 X 14 (base) X 55 (distal end). Total 
length to tip of perithecium largest, 800 /x. 

On abdomen of Qaedius nov. sp. New Zealand. Sharp Collection, 
No. 1159. 


Receptacle two-celled, bearing an antheridial branch terminally and 
a single perithecium laterally. Antheridium consisting of several super- 
posed cells from which single simple antheridia are borne directly. The 
perithecium borne on a stalk, the lumen of which becomes continuous 
with that of the ascigerous cavity. 

Acompsomyces Corticariae nov. sp. 

Receptacle narrow below, distally enlarged, hyaline ; the subbasal cell 
• small. Basal cell of the appendage brown, distally narrowed to the base 
of the appendage proper, which is brown, and consists of three sym- 
metrical cells, the upper smaller, becoming a terminal antheridium, the 
lower bearing several antheridia somewhat irregularly. Perithecium 
brown, rather abruptly distinguished from the short hyaline stalk ; the 
tip very broad and darker ; the lip-cells forming four hyaline-tipped, 
nearly symmetrical papillae, which terminate four corresponding ridges. 
Spores about 30 X 2 u. Perithecia 90 x 26 jx, the stalk 15 /x. Recep- 
tacle 25 /x. Antheridial appendage, above stalk-cell, and including 
terminal antheridium, 40 «. 

On elytron of Corticaria sp. Berkeley, California. 

STICHOMYCES nov. gen. 

Receptacle consisting of two cells, the upper bearing one or more 
stalked perithecia laterally, and an antheridial appendage terminally. 
The appendage consisting of several superposed cells, the lowest sterile, or 
having one or two opposite lateral perithecia; those above it bearing 
opposite lateral branchlets distally, the series ending in a terminal sterile 


branch. Antheridia simple, flask-shaped, free, borne in small groups on 
short branchlets. 

Stichomyces Conosorriae nov. sp. 

Dull amber brown. Receptacle and appendage undifferentiated, the 
basal cell of the former small, triangular in outliue ; the subbasal cell 
about as broad as long, and similar to the cells of the appendage, bearing 
distally and laterally a single perithecium, sometimes two, which are then 
paired on opposite sides of the cell, like the antheridial branchlets. Ap- 
pendage consisting of five superposed subequal cells slightly longer than 
broad, the basal one sterile, or rarely (abnormally) producing one or two 
perithecia as in the subbasal cell below it : the three cells above slightly 
larger, the upper angles separated by oblique septa to form small cells 
on either side, which bear short one or few celled antheridial branchlets ; 
the terminal cell somewhat smaller, bearing a simple terminal several- 
celled branch in addition to the lateral branchlets, all of which appear to 
be sterile. Antheridia with broad necks grouped in twos or threes. 
Perithecium darker brown, more or less symmetrically inflated ; the tip 
hardly modified; the basal cells collectively broader and nearly as long 
as the stalk-cell. Spores 35 X 2.5 fx. Perithecia 85 X 25 /x, the stalk- 
cell 36 x 1 t /x. Total length to tip of the appendage proper 150 «, the 
terminal branch 150 fx, the antheridial branchlets about 20 /x. Total 
length to tip of perithecium 185-200 ft. 

On Conosoma pubescens Payk. Belmont and Waverly, Mass. First 
observed by Mr. Dullard. 

Rhachomyces Oedichiri nov. sp. 

Receptacle strongly curved, rather short, the lower cells especially 
more or less suffused with clear brown, the basal cell slender, the cells of 
the main axis above it successively larger, about ten to twelve in all. 
Appendage hardly ever reaching to the tip of the perithecium; the shorter 
margin alone subulate and straight, the rest appressed, denser toward the 
base of the perithecium, where they form a tuft which does not wholly 
surround it, curved slightly outward, somewhat attenuated; tips abruptly 
recurved or subhelicoid. Perithecium somewhat inflated, hyaline, with 
the exception of several longitudinal dark brown marks at the tip, the 
base concealed by the appendages. Spores 36 X 4 m. Perithecia 90- 
1 10 X 30-35 (i. Total length to tip of perithecium 220-250 /x. Long- 
est appendages about 90 u. 

On Oedichirus nov. sp. Rio de Janeiro, Brazil. Sharp Collection, 
No. 1154. 


Rhachomyces Glyptomeri nov. gp. 

Receptacle slender, dirty translucent brown, the main axis coi 
of about seven cells (below the lower of the two perithecia which are 
present in the type; : the appendages -lightly divergent, large and long, 
opaque brown, flexed inward near their hyaline, somewhat more Blender 
extremities, and extending beyond the tips of the perithelia. Perithecinm 
short-stalked, -trongly curved, slightly inflated, hyaline, -oiled with brown- 
ish, the dps well distinguished, blackish brown and obliquely truncate. 
Perithecia, including basal and stalk-cells, about 185 / 41 /v.. Receptacle 
to base of lower perithecinm 100 / 15 /*. Appendage-, long 60/* 

or more. 

On tip of abdomen of Glyptomerta cavicolus MulL Carniola, Austria. 
Sharp Collection. No. 1111. 

Rhachomyces Dolicaontis nov. sp. 

Form elongate. Cells of the main axis of the receptacle- twenty to 
thirty-five, more or less dirty brownish, banded with dark blackish br< 
below, while the more slender proximal cells are usually opaque ; the axis 
of nearly equal diameter throughout and nearly -traight above about the 
eighth cell; each cell containing distally one, the axis cells two, roundish 
or oblong brown bodies ''possibly thickenings of the walls; which 
the stigmata of an insect larva. The appenda* .hat divergent, 

opaque, except a narrow upper hyaline margin, short, stiff and numerous ; 
those external more slender, slightly curved and sharply pointed ; th 
between somewhat stouter and longer, with -lightly recurved tips; th 
about the base of the perithecium, which they do not conceal, but slightly 
longer and few in number. Perithecinm -hort-stalked, slightly more 
or less symmetrically inflated, dull brown, minutely punctate or irrarmlar, 
not uniformly suffused ; the tip with darker shades, the blunt apex 
hyaline. Spores 66 / 5 a. Perithecia 150-200 X 42-60/*, including 
the basal and stalk-cells. Larger appendages 90-110 /t, smaller about 
7o/y.. Total length 600-1100/*, the- average diameter about 30-35//. 
On all parts of Dolicaon Lathrobioidei Casteln. Cape of Good If 
Africa. Sharp Collection. No. 1146. Berlin Museum, No- 833 and 

Sphaleromyces Quedionuchi nov- 

Perithecium relatively small, translucent, tinged with amber brown, 
straight, very slightly almcrst symmetrically inflated ; the tip hardly dis- 


tinguished ; one of the lip-cells forming a blunt, terminal, irregularly 
curved, hyaline, sometimes abruptly distinguished projection, below the 
base of which arises on the inner side a tongue-like outgrowth externally 
and basally blackish brown, the broad rounded hyaline end of which is 
curved against or across the base of the terminal outgrowth; the stalk- 
cell small, the basal cells collectively larger, and separated from it by a 
very oblique septum. Basal cell of the receptacle long, black, obconical, 
the narrow base translucent ; the subbasal cell small, nearly triangular. 
Appendage consisting of five very obliquely superposed cells, the two 
lower nearly equal, the cells ahove successively smaller, but equal in 
length ; the branches which are once or twice branched and extend about 
to the middle of the perithecium, arising from the whole surface of their 
inner margins, the terminal cell soon destroyed. Spores 55 X S /x. 
Perithecia 135 X 36/a. Basal cell of receptacle 120 fx. Appendage 
without branches 55 //.. Total length to tip of perithecium 290-310 jx. 
On the abdomen of Quedionuchus impunctus Sharp. San Andres, 
Vera Cruz. Sharp Collection, No. 1105. 

Sphaleromyces Chiriquensis nov. sp. 

Almost uniformly translucent dirty amber brown. Perithecium very 
large and crowded with spores, long, with a very slight general inflation, 
the base narrower, tapering abruptly at the short tip : one of the lip-cells 
forming an erect, median, straight, hyaline, cylindrical or slightly in- 
flated, nearly truncate terminal projection, which is subtended by a 
posterior or partly lateral, somewhat larger, spine-like, slightly diver- 
gent, deep black brown, nearly straight or slightly outcurved pointed 
outgrowth, its tip nearly on a level with that of the median projection : 
the basal cells collectively slightly larger than the short stalk-cell, and 
not distinguished from the base of the perithecium. Basal cell of the 
receptacle very large, tapering throughout from the broad distal to the 
narrow basal end, paler than the small, flattened, deeper brown subbasal 
cell. The appendage consisting of a relatively large basal stalk-cell, 
which is slightly longer than broad, and partly united to the stalk-cell 
of the perithecium; above are four short successively smaller cells, their 
septa slightly oblique, the three lower bearing branches as usual, which 
may branch once above their basal cells, the branchlets brown, erect, 
rigid, closely aggregated ; the uppermost cell paler, with a terminal 
branch. Spores 50 X 2 /x. Perithecia 220-250 X 40-48 fx, to tip of 
median projection, the subterminal process 25 X 7 p; the stalk-cell 35 
X 25 p. Receptacle 240 X 40 jx, the basal cell 220 fx. Total length to 


tip of perithecium 500-600 //.. Appendage without branches, including 
stalk-cell, 75 p. 

On the tip of the abdomen of Quedius flavicaudus Sharp. Volcan 
de Chiriqui, Panama. Sharp Collection, No. 1157. 

Sphaleroniyces Indicus now sp. 

Perithecium relatively very long and large, yellowish, very slightly 
inflated toward the base, tapering very gradually to the broad, blunt tip 
which is subtended by a truncate, conical lateral projection ; the stalk- 
cell relatively short. Receptacle relatively small, the two cells nearly 
equal, the upper bearing the stalk-cell of the perithecium terminally and 
the basal cell of the appendage laterally ; the latter overlapping it to its 
base. Appendage consisting of four superposed cells, the basal (stalk- 
cell) small, triangular ; the two cells above it larger and longer, bearing 
short antheridial branches from the upper inner angles ; the terminal 
cell smaller, subcorneal, bearing a small terminal branchlet. Spores 
about 44 X 4 /a. Perithecium 290-340 X 45 ft, the stalk-cell 72 /x. 
Receptacle 55^. The appendage 125 /a. 

On the upper surface of the tip of the abdomen of Pinophilus (near 
"P. rufipennis"). Malabar, India. Sharp Collection, No. 1151. 

Corethromyces Latonae nov. sp. 

Perithecium reddish brown with a purplish tinge, often straight, or 
externally concave, slightly inflated ; the lip-cells forming a small short, 
slightly bent, nearly cylindrical, truncate, or papillate terminal projection, 
which is rather abruptly distinguished ; the secondary stalk-cell, and the 
basal cell above it, bulging outward more or less prominently, and 
separated by a rather conspicuous irregular indentation : the stalk-cell 
small and squarish. The basal cell of the receptacle asymmetrical ; its 
anterior margin straight and perpendicular, the posterior slightly curved 
and oblique ; its distal margin oblique with a posterior protrusion ; its 
slender base translucent, but otherwise opaque, the opacity involving a 
portion of the small flattened subtriangular subbasal cell. The appendage 
consisting of a series of about five successively smaller hyaline cells, the 
lowest greatly flattened ; the series above, the distal cells of which soon 
disappear, often turned outward so as to become almost horizontal in 
position, giving rise from their inner sides to numerous hyaline branches, 
which may be more or less copiously branched. Spores about 35 X 2 fx. 
Perithecium 90-105 X 20-25 ^, the stalk and basal cells together 20- 


25 fj.. Receptacle 110 X 50 (distal end) X 10 /x (base). Total length 
to tip of perithecium 225-250 /x. 

On the legs and abdomen of Latona Spinolae Guer. Bogota, Colum- 
bia. Berlin Museum, No. 834. 

Corethromyces Stilici nov. sp. 

Perithecium amber colored, with a faint brownish or reddish tinge, 
somewhat irregular in outline through a spiral twist in the wall-cells, 
which are distinguished from one another by slight furrows ; slightly 
inflated toward the base, tapering to the broad blunt apex ; the tip not 
at all distinguished ; the basal and stalk-cells well developed, hyaline, the 
latter bent abruptly upward from its insertion. Basal cell of the re- 
ceptacle small, hyaline on the anterior side just above the foot, but 
otherwise blackish brown or opaque, bulging posteriorly above the foot ; 
distally and posteriorly pi'oliferous to form a straight, black, blunt finger- 
like outgrowth, which lies external to the appendage ; the subbasal cell 
nearly hyaline, subtriangular, separated from the basal cell by a very 
oblique septum. Appendage hyaline, consisting of a nearly free and 
nearly isodiametric stalk-cell, above which are three or four cells which 
produce a close tuft of hyaline brauches on the inner side. Spores about 
30x3^. Perithecia 80-85 x 22 /x, its stalk-cell 30 X 18 p. Recep- 
tacle 25 fx, the outgrowth 55 X 7 /x. Appendage, including branches, 
50 /x. Total length to tip of perithecium 150 ai. 

On the abdomen of Stilicus sp., Interlaken, Switzerland. On Stilicus 
ruftpes Germ., Berlin Museum, No. 836. Europe. 

Ceratomyces spinigerus nov. sp. 

Bright amber brown. Perithecium paler anteriorly, about twenty- 
eight wall-cells in each row; narrower at the base, the lower half 
bulging anteriorly, tapering distally where it is rather strongly curved 
away from the antheridial appendage : the tip hyaline, prominent, obtuse, 
about half as long as the curved tooth- or spine-like one-celled deep 
amber brown appendage, which arises below and beside it. Basal cell 
of the receptacle large, long, mostly curved, broader distally, opaque ; 
the portion above it relatively small and narrow, concolorous with the 
perithecium. The appendage erect, slightly divergent, stiff, long, slender, 
rather remotely septate, but the basal cell often broader than long, about 
seven-celled, tapering distally. Spores 90 X 4 /x, in one small specimen 
165 x 4.5 /x. Perithecia 425-500 X 70-95^, the appendage 45-50 tt. 


Receptacle 1 75-220 /x, the basal cell 150-170 /*. Antheridial appendage 
200-325 fx. 

On the inferior anterior margin of the thorax near the base of the right 
elytron of Tropisternus apicipalpis Cast. Jalapa, Mexico. Sharp Col- 
lection, No. 1178. 

Ceratomyces procerus nov. sp. 

Rather pale amber brown. Perithecium very elongate, of nearly 
equal diameter throughout, the wall-cells in each row more than sixty 
in number ; the conformation at the tip similar to that in O. confusus ; 
the perithecial appendage erect, short and stout, consisting of about ten 
cells, distally curved outward, tapering from its broad base to the bluntly 
pointed tip. Appendages (broken) and receptacle much as in C. con- 
fusus. Perithecium 800-850 X 65 /x, its appendage 125 /x. Total length 
to tip of perithecium more than one millimeter. 

On the inferior surface of the abdomen (near the middle) of Tro- 
pisternus sp. San Fidelio, Brazil. Museum of Comparative Zoology, 
Cambridge, No. 1338. 

Ceratomyces curvatus nov. sp. 

Amber brown. Perithecium relatively large, inflated toward the base; 
the distal half up to the perithecial appendage of about equal diameter 
throughout ; about forty cells, more or less, in each row of wall-cells ; 
the configuration at the tip very similar to that in C. confusus, the tip 
itself more prominent, the apex more pointed ; the perithecial appen- 
dage about nine-celled, the distal half pale, curved or recurved, broader 
below, shorter and stouter. Receptacle much as in C. confusus, the basal 
cell black, the further suffusion somewhat less extensive. Appendage 
consisting of about six or seven cells, tapering distally, rather short. 
Spores about 70 X 4 /x. Perithecia 500-615 X 75 [x (below) X 60 /x 
(distally), the appendage 150^. Total length to tip of perithecium 
600-700 (i, to tip of antheridial appendage about 250 /x. 

On Tropisternus Caracinus N. on inferior surface of abdomen near 
the tip. Caracas? Berlin Museum, No. 1057. 

Ceratomyces Mexicanus nov. sp. 

Dark amber brown. Perithecium with a slight submedian inflation ; 
distally broad, the outer margin turning abruptly inward distally to the 
inconspicuous retracted tip, which lies close at the base of the perithecial 
appendage, and is externally subtended by irregular inconspicuous papil- 


late protrusions : the basal cell of the appendage slightly divergent, 
several times as long as broad ; the external margin straight, the inner 
strongly concave with a median blackish suffusion; the rest of the appen- 
dage slightly curved, about eight or nine-celled, tapering slightly and 
diverging strongly above the basal cell. The antheridial appendage and 
the receptacle much as in C. mirabilis. Spores 85 X 5 fi. Perithecia 
400-175 x 110-125 fi, the appendage about 290 //, its basal cell 70 X 26 
and 36^. Total length to tip of perithecium 550-640 p. 

On the left inferior margin of the abdomen of Tropistemus nitidus 
Sharp, Sharp Collection, No. 1177, and of T. chalybeus Cast., British 
Museum, No. 772, Oaxaca, Mexico. 

Ceratomyces Braziliensis nov. sp. 

Dark amber brown. Perithecium somewhat inflated just above the 
constricted base, the upper two-thirds broad and of about the same 
diameter throughout; about forty-five wall-cells in each row, the tip 
small, short, rather narrow, abruptly hunched externally, the hyaline 
lips turned abruptly toward the base of the perithecial appendage, which 
consists of a basal cell hardly differentiated from the wall-cell below it, 
though somewhat longer, the portion above it erect, slender, stiff, slightly 
curved outward, tapering but little, the subbasal cell bearing a charac- 
teristic basal enlargement which projects toward the lip-cells and lies 
just above them. The appendage and receptacle much as in C. mira- 
bilis. Perithecium 650 X 95 ju (basal) X 87 ^ (distal). Appendage 
185 ix, or more. Total length to tip of perithecium 800 p. 

On inferior thorax of Tropistemus nitens Cast. var. Rio de Janeiro. 
Sharp Collection, No. 1181. 

KAINOMYCES nov. gen. 

"Receptacle much as in Zodiomyces, broad and flattened ; consisting of 
a single basal cell and typical foot, above which the successive cells 
become variably divided by longitudinal septa into transverse cell-rows 
or tiers : the distal portion more or less definitely distinguished and con- 
sisting of superposed cells, the lowest of which alone become longitu- 
dinally divided, all producing laterally antheridial (?) branches : several 
of the tiers immediately below this appendiculate portion growing out 
laterally at right angles to the main axis of the receptacle on one or 
both sides to form "perithecial branches" consisting of superposed cells 
and terminated by solitary perithecia. The perithecium of peculiar 


form, with six wall-cells in each row in addition to the lip-cells ; the 
base of the trichogyne persistent in the tbrui of a peculiarly modified 
unicellular appendage. 

It has proved impossible from an examination of the available material 
of this extraordinary form, to determine the character of the antheridia; 
yet there can hardly be any doubt as to its true position among the 
" Exogenae " near Zodiomyces, Euzodiom^ces, and Ceratomyces, its dis- 
tal appendiculate portion being evidently homologous with the "appen- 
dage " of the last-mentioned genus. 

Kainomyces Isomali nov. sp. 

Receptacle variably developed below the distal appendiculate portion, 
sometimes very broad, often much narrower : the cells above the basal 
cell becoming broader and flattened, and soon divided longitudinally by 
one or more septa, nearly hyaline and broadly edged wholly or in part 
below, especially on the posterior side, with contrasting brownish black, 
which may involve the whole of the cell, except the transverse septa; 
the blackened area usually characteristically indented above, and some- 
times involving all but the uppermost tiers. Perithecial branches vari- 
ably developed, the free portion curving upward, and consisting of from 
about twelve to thirty-five superposed hyaline cells, which are more or 
less flattened, usually separated by slight constrictions, the distal one 
similar to the others and followed directly by the basal cells of the 
perithecium. Perithecium becoming tinged with pale amber brown, 
usually short, stout and suboblong, often not distinguished from its 
basal cells ; the distal end abruptly rounded, the pore subtended by a 
tooth-like outgrowth, half as long as and paler than the trichogynic 
appendage, which bears a slight resemblance to a duck's bill, is dark 
clear brown, somewhat narrower distally and pale tipped, broader toward 
the base, where it is abruptly constricted and hyaline. Spores about 
30 X 3.5 jte. Perithecia 72-80 X 40-50 ^ exclusive of trichogynic ap- 
pendage, which measures 28-32 X 11 fi. Perithecial branch 100-253 p. 
Receptacle 150-220 X 40 60 p. Antheridial branches about 50 p. 
Total length to tip of perithecium 250-460 ft. 

On Isomalus Conradti Fauvel. Derema, Usambara, East Africa. 
Berlin Museum, Nos. 847-848. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 3. —Junk, 1901. 


By Gilbert Newton Lewis. 

By Gilbert Newton Lewis. 

Received April G, 1901. Presented by T. W. Richards, April 10, 1901. 


The many-sided application of thermodynamics to physical chemistry 
in recent years has led to a maze of mathematical expressions which is 
bewildering to the beginner and confusing even to the initiated. The 
great majority of these physico-chemical formula; arc based not only 
upon the two laws of thermodynamics but also upon some empirical law 
or approximation, and are as a rule not rigorously true, but are useful in 
so far as the system considered does not deviate too widely from certain 
ideal conditions. The difficulty of treating mathematically equations 
which are not strictly exact is probably the chief reason for the con- 
tinued separate existence of the large number of formulae which, though 
not identical, are tantalizingly similar in form. It seemed probable that 
if the present formulae could in any way be replaced by rigorously exact 
ones, without sacrificing concreteness or immediate applicability, then 
these exact equations might be so systematized that one might serve 
where a number of isolated equations are now in use, with a great gain 
in simplification. With this object in view the present investigation has 
been carried on, and with the unexpected success of finding a single law 
which is simple, exact, general enough to comprise in itself many laws 
and yet concrete enough to be immediately applicable to specific cases. 
The following development will be based upon four laws of nature and 
upon no other hypothesis or assumption of any kind. These laws are 
the following : — 

1. The first law of thermodynamics. 

2. The second law of thermodynamics. 

3. Every gas, when rarefied indefinitely, approaches a limiting condi- 
tion in which 

Pv = RT, (1) 

if P represents pressure; v, molecular volume; R, the gas constant; T, 
the absolute temperature. 



4. Every solution diluted indefinitely approaches a limiting condition 
in which 

n v = R T, (2) 

if II represents osmotic pressure. 

The present paper will discuss the laws which govern systems com- 
posed of a single, chemically simple, substance, and will be followed by a 
second paper in which the laws governing mixtures will be studied. 


Clausius' Formula Simplified. • 

Clausius showed that if Q represents the heat change in a reversible 
change, the second law of thermodynamics may be expressed by the 

Q _dQ 

which is valid for every cyclic process ; moreover, that since in a cycle 
there is no change in internal energy, d Q represents the work of the 
cycle, and that when the process is one in which the system undergoes a 
finite change of volume at constant pressure, and no other work is done, 

dQ = dP(V 1 -V 2 ), 

where P represents the pressure and V l and V. 2 the original and final 
volumes. In the specific case in which the system is composed of a 
liquid and its vapor we obtain the equation 

Q _ pi — vt) dp 
' T~ dT ' 

in which p represents vapor pressure ; Q, the total heat of vaporization 
of one gram-molecule ; and v x and v 2 , the molecular volumes of vapor and 
liquid respectively. Transposing the equation gives an expression for 
the change of vapor pressure with change of temperature, 

d T (», - v 2 ) T W 

This equation of Clausius is both general and exact, but in practice it 
is replaced by a simpler equation, which is derived from it if two 
assumptions are made : First, that r 2 is negligible compared with v u and 
therefore approximately, 

t'i — V 2 = Vi. 


Second, that the vapor obeys the gas law, 


i\ — 

These two equations substituted in (4) give the familiar equation, 

d In p _ Q 

dT ~ RT Z 


While neither of the two assumptions made above is in any case 
strictly true, they differ in that the second represents a true limit as the 
vapor approaches the perfect gas in its behavior, but the first is always 
mathematically absurd, for the volume of a liquid cannot be made to 
approach zero even as a limit. For an exact equation, therefore, we 
must return to equation (4), notwithstanding its rather complicated form. 
There is in fact a lack of simplicity in this equation which does not 
appear in certain analogous expressions that will be developed in this 
paper. That this lack of simplicity is, however, not inherent in every 
exact equation for the influence of temperature on vapor pressure, but is 
due rather to the complex conditions for which equation (4) is proved, 
will be evident from the following considerations. 

It is well known that at constant temperature the vapor pressure of 
any substance is changed by a change in the total pressure on its surface, 
according to the equation first obtained by Poyntiug,* 

i£ = % ( 6) 

dP v x 

in which p represents vapor pressure ; P, total pressure ; v. 2 and v h mo- 
lecular volumes of liquid and vapor respectively. When, therefore, the 
temperature of a liquid is raised, the resulting increase in vapor pressure 
brings an increase in the total pressure on the surface, and this in itself is 
a cause of further change in vapor pressure. The observed change in 
vapor pressure is the sum of the change due merely to temperature 
change and the change due to the change in total pressure upon the 
surface. Let us therefore determine the change in vapor pressure with 
change of temperature when the total pressure on the surface is kept 
constant by artificial means. Figure 1 represents such an arrangement. 
The space E D contains liquid kept at constant pressure by a piston, F. 
B D contains an inert insoluble gas. B C is a membrane impermeable 
to this gas, but permeable to the vapor of the liquid used. A B contains 

* Phil. Mag., (5) XII. 32 (1881). 



this vapor alone. A change of temperature will change the vapor pres- 
sure in A B without changing the total pressure on the liquid, which 
is always equal to the outside pressure on F. We may simplify this 
arrangement by making the layer of inert gas so thin that it may be 
regarded together with the membrane B C merely as a single membrane, 
which is impermeable to the liquid but permeable to the vapor. In 




Figure 1. 

Figure 2. 

Figure 2 it is represented by the dotted line B. The spaces B C and A B 
are filled with liquid and vapor respectively, and the pistons A and C can 
be moved up and down so as to distribute the substance between the 
liquid and gaseous phases as desired. The whole is removed from the 
influence of gravity. Let us start with one gram-molecule of the sub- 
stance, all in the liquid state, and pass through the following reversible 
cycle, during which the pressure, P, upon the piston, C, remains constant, 
while the pressure upon A is always kept equal to the vapor pressure. 
At first the piston A is at B ; the space B C has the volume v 2 . (1) The 
temperature is raised from T to T + d T, the pressure on A being raised 
at the same time from p, the original vapor pressure, to p + dp, so that 
none of the liquid evaporates. The piston C moves down on account of 
the expansion, dv 2 , of the liquid. (2) All the liquid is evaporated at 
temperature T -f d T, C moving to B, and A moving up to furnish the 
volume, v v (3) The temperature is again brought to T; the pressure 
on A to p. A moves down on account of the contraction di\. (4) All 
the vapor is condensed and the original condition is restored. The 
amounts of work done by the system in the several steps are : — 

W l = Pdv 2 , 

W 2 = -P(v 2 + dv 2 ) + (p + dp) Oi + dvj, 

W 3 = — p dv u 

Wi = Pv 2 — pv v 


The total amount of work gained, the sum of these terms, is equal to 
the total amount of heat transformed into work, that is, 

W t + IF 2 + W z + W i = dQ = ^dT, 
from equation (3). Adding the terms we obtain, 

v i d P = j. dT > 

or writing so as to express the constancy of P, 

9Tj P ~ Vl T' 



This important result may be derived directly from equations (4) and 
(6) and for solids as well as liquids. Since the vapor pressure is a func- 
tion of the temperature, T, and the pressure on the surface, P, we may 

Now, in general, when only a pure substance and its vapor are present, 
the change in pressure on the surface of the substance is merely the 
change in vapor pressure, that is, 


Moreover, ( y^ j = — , from equation (6), therefore, 

it 7) 

Substituting for -r— from equation (4), 

Tfr-vjy vJ-\9Tj P ' 0T \9TJ P v x T y 

which is equation (7). "We have in this equation a marked simplifica- 
tion of the Clausius formula with no loss of exactness. We could now, 
by making the single assumption that the vapor obeys the gas law, throw 
equation (7) into the form analogous to (5), namely, 


\9T ) P - 

RT 2 


Instead of using this equation we may introduce here a quantity with the 
aid of which it is possible to substitute for approximate equations of the 
type of (7) other entirely exact equations of the same form. This 
quantity is one whose utility I have shown in a recent paper.* It 
may be well to repeat and amplify the definition there given. 



If any phase containing a given molecular species is brought in contact 
with any other phase not containing that species, a certain quantity will 
pass from the first phase to the second. Every molecular species may 
be considered, therefore, to have a tendency to escape from the phase in 
which it is. In order to express this tendency quantitatively for any 
particular state, an infinite number of quantities could be used, such, for 
example, as the thermodynamic potential of the species, its vapor pres- 
sure, its solubility in water, etc. The quantity which we shall choose is 
one which seems at first sight more abstruse than any of these, but is in 
fact simpler, more general, and easier to manipulate. It will be called 
the fugacity.f represented by the symbol if/ and defined by the following 
conditions : — 

1. The fugacity of a molecular species is the same in two phases when 
these phases are in equilibrium as regards the distribution of that species. 

2. The fugacity of a gas approaches the gas pressure as a limiting 
value if the gas is indefinitely rarefied. In other words, the escaping 
tendency of a perfect gas is equal to its gas pressure. 

That these two conditions are sufficient to define a property of every 
substance which is not a mathematical, fictitious quantity, but a real 
physical quantity, capable of experimental determination in every case, 
must now be shown. It is obvious from the above conditions that in any 
case where our present methods of measurement are unable to show a 
deviation of the vapor of a substance from the gas law then the vapor 
pressure is the nearest approximation to the fugacity. In all cases the 
vapor pressure is an approximation to the fugacity, the approximation 
being nearer the nearer the vapor is to a perfect gas. When the 

* Proc. Amer. Acad., XXXVI. 145 (1900) ; Zeit. Phys. Chem., XXXV. 343 (1900). 

t In the earlier paper this quantity was called the escaping tendency and repre- 
sented by the same symbol. For the sake of brevity I have chosen to substitute 
the word " fugacity " for " escaping tendency " without the slightest change in the 
meaning of the function. 


behavior of the vapor deviates perceptibly from that of the perfect gas 
the exact value of the fugacity may be found as follows : — 

From the four laws stated in the introduction it is easy to derive the 
following, which is a rigorous statement of Henry's law, namely : The 
coefficient of distribution between a gas and its solution at constant tem- 
perature approaches a constant with increasing dilution. This constant 
will be designated by p. At infinite dilution, 

P _ 

where p is the gas pressure and II the osmotic pressure in solution. 

Now p, at infinite dilution, is equal to the fugacity of the substance in 

the gaseous phase, and also in the solution, since the two phases are in 

equilibrium. Therefore, 

if/ = P n. (8) 

That is, the fugacity of the solute in an ideal solution is equal to its 
osmotic pressure multiplied by p. If now it is desired to find the 
fugacity of any molecular species X in any given phase, that phase may 
be brought in contact with a chosen solvent and the osmotic pressure 
Ili of the saturated solution determined. Then by diluting this solution 
in contact with vapor of X the limit p x of the distribution ratio may be 
found and so the product p x IIx. So for another solvent we may find the 
product p 2 n 2 ; for a third, p s H 3 , etc. These will all be equal except in 
as far as the saturated solutions deviate from the ideal solution. Prac- 
tically, the product will be the same for all solvents in which X is only 
slightly soluble and will be the fugacity of X. Theoretically, the exact 
value of the fugacity is the limit approached by the product, p II, as sol- 
vents are successively chosen in which X is less and less soluble. 

We see, therefore, that fugacity is a real physical quantity capable in 
all cases of experimental determination. A complete appreciation of the 
meaning of this quantity is essential for the understanding of the follow- 
ing pages. In order, however, not to distract attention further from our 
main object, a further discussion of fugacity will be postponed to the last 
section of this paper, in which another independent method for the 
determination of if/ will be offered, using only such quantities as have 
already been determined in many cases. 

The great utility of this new quantity will be shown to lie in the fact 
that the approximate equations containing the vapor pressure and 
developed rigorously except for the assumption that the vapor pressure 
obeys the gas law, may be replaced by exact equations of the same form 


or of equal simplicity containing the fugacity instead of the vapor 
pressure. Let us proceed to the determination of the laws according 
to which fugacity changes with changes in the variables upon which 
the condition of a substance depends, considering in the present paper 
only those systems which are composed of a single chemically simple 


Influence of Temperature and Pressure on the Fugacity. 

Let us consider two' phases of a substance at the same temperature 
and pressure, but not necessarily in equilibrium with each other. A 
solvent may be chosen in which both phases are soluble without molecu- 
lar change, and to so slight an extent that the saturated solutions may 
be regarded as infinitely dilute. In such a case the solubility of each 
phase is governed by the following equation, which may be obtained 
directly from equations (2) and (3), 

/cHn_n\ _Q_ 

\ 9T ) P R T 2 ' 

in which II is the osmotic pressure of the saturated solution and Q the 
reversible heat of solution (that is, inclusive of the osmotic work). We 
may write for the two phases, 

{-JT-) P = RT* aud VJT-) P = RT» ° r COmbimng > 

Qx - Q, (9) 

1t no 
91a u 2 


RT 1 

Q x — Q 2 may be conveniently replaced in the following way. Let one 
gram-molecule of the first phase be dissolved in the solvent, this solution 
then diluted or concentrated to the osmotic pressure II 2 , and then the 
gram-molecule removed as the second phase. If these three steps be 
done reversibly the heat absorbed in each will be respectively 

&, RT\u^, -<? 2 . 

The total heat change is a function only of the conditions of the two 
phases, not of the path by which one passes into the other, and may be 
designated by Q h2 , thus, 



Qi, 2 = <?i + R Tin -+ [ - - <?.,, or Q, - Q, = Q lfi -RTln^- 

"2 II9 

We may therefore write equation (9) as 


9 In 


3 7' 

<?i, 2 



i2 T* T 

Since we are dealing with infinitely dilute solutions in the same solvent, 
ij/ l = pUi and $2. = p n 2 , therefore 

— = — - , and the above equation becomes 
«A 2 n 2 

9 In 


_}h I 

P? 1 J, 





This is the desired equation connecting temperature and escaping 
tendency. Its form can be simplified by a slight rearrangement. 

Considering the quantity yin — we notice that 





d In — 

+ ln^,or 


<A 2 

Combining this equation with (10) gives 


T 5 

Prin^ 1 




3 Tin 


3T 7 


Leaving in this form for the present the equation connecting tempera- 
ture and fugacity at constant pressure, let us determine the influence of 
pressure on the fugacity at constant temperature. I have already dis- 
cussed this question in a previous paper,* but instead of using the 
general equation there derived it has seemed preferable to base all 
the reasoning of this paper directly upon the four laws stated in the 

Let us consider any simple substance and a solvent, so arranged t 
that the pressure upon the substance in question may be altered without 

* Loc, cit. 

t Several such arrangements are described in the paper just mentioned. 


changing the pressure on the solvent and without preventing the sub- 
stance from passing freely into or out of the solvent. The osmotic 
pressure of the saturated solution depends upon the pressure on the 
substance. If the latter is represented by P and the former by II, then 
for P -f d P the osmotic pressure will be II + d II. We may moreover 
represent the molecular volume of the substance by v at pressure P, 
by v — d v at pressure P + dP; the molecular volume in the solution 
by v' at osmotic pressure II, by v' — d v' at II + d II. If a gram-mole- 
cule of the substance at pressure Pis (1) dissolved against the osmotic 
pressure II, (2) its solution concentrated to II -f d II, (3) removed from 
solution against the pressure P + d P and (4) allowed to expand from 
P + d P to P, an isothermal cycle is formed, and if each step is made 
reversible the total work of the cycle is zero. The work obtained in the 
several steps may be represented by W x , W 2 , etc. 

W x = 1TV - Pv, 
Wz = -Ildv>, 

w 3 = (P + d P) (v - dv) - (n + d n) 0' - dv<), 

W i = Pdv. 

Writing the sum equal to zero, 

vdP— v'dU = 0, 
or expressing in the equation the constancy of T, 

(3n\ v_ 
\dPJ T ~ v<' 


This is an exact general equation connecting the osmotic pressure of a 
saturated solution and the pressure upon the pure solute. It is entirely 
analogous to equation (6). Since we may choose a solvent in which the 
solute is as slightly soluble as desired we will choose one in which the 
solution may be regarded as infinitely dilute. Then, 



from equation (2). Combining this equation with (12) we obtain 

From equation (8), t/r = p II. Therefore In \p = In II + In p, and 

\JP~)*~~ \9P Jt 



since p is constant at constant temperature. Hence equation (13) 

/9 In i/A v 

\~9~p~ ) T = ln 


Subtracting two such equations we obtain an equation for two phases, 





Vl — Vj 




The General Law of Fugacity. 

Equations (11) and (15) show a similarity which may be made more 
striking by a few simple transformations. In equation (11) Q lfi> the 
heat absorbed in any reversible transformation of the substance from 
the first to the second state is equal to the difference in entropy 
between the second state and the first, multiplied by the absolute tem- 
perature ; that is, —p~ = — (Si — S 2 ), 

where S t and S 2 represent the entropy of the first and second states 

Substituting in equation (11) and transposing the constant R, we 




= _ ( Sl _ S. 2 ). 


In equation (15) R T is constant, and may be transposed, bringing 
the equation into the form, 





J T 

= vi — y 2 - 


The symmetry of equations (16) and (17) with regard to the quan- 
tities T and — S on the one hand, and P and v on the other hand, is 
perfect. This similarity is peculiarly interesting in the light of the 
brilliant theory of Helm, according to which two quantities are funda- 
mentally connected with each kind of energy, the one its intensity, the 


other its capacity.* Thus, for example, pressure, surface tension, elec- 
trical, potential, and temperature are considered to be the intensities 
concerned in energy changes in which the corresponding capacities are 
respectively volume, surface, quantity of electricity, and entropy. We 
may denote in general the intensity of any energy by /and its capacity 
by H. If we substitute / and H for /and S in equation (16) and for 
Pand v in (17), the equations become identical except for the minus sign 
in (16). We are thus led to suspect the existence of a general equation 
of the form 

{dR Tin & 


I 91 

J r,r> 

F7 H < 18 > 

and further, of the equation for a single phase, 

This equation would mean that if the fugacity is a function of a number 
of energy intensities, I, /', /", etc., the rate of change in the quantity 
.R, with a change in one of the intensities alone, is equal to the 
corresponding capacity. In other words, this equation, if true, expresses 
a law so far reaching that it embraces every possibility of the change of 
state of any simple substance under all conceivable conditions. Let us 
examine the validity of this equation for all cases in which the escaping 
tendency can be shown to be influenced by the intensities of various 


The influence of pressure is given in equation (14), which may be 

and therefore conforms to equation (19). 

* These quantities have been hitherto called the factors of energy, and their 
product has been written equal to the quantity of energy concerned. I believe 
that this part of the theory is absolutely unjustified by the facts, and that it has 
been the chief cause of the hostility which has been shown to a conception which 
is valuable in research and has proved a veritable boon in the pedagogical treat- 
ment of energetics. I hope soon in another paper to discuss this whole question, 
especially in the light of the results of the present paper. Meanwhile we may 
speak of intensity and capacity as the dimensions of energy, signifying that their 
product has the dimensions of energy. 


The influence of temperature is expressed for two states simultane- 
ously in equation (1G), which conforms to equation (18) except for the 
minus sign. This slight difference might be explained away, but a much 
weightier difficulty confronts us when we attempt to split equation (1G) 
into two equations, each expressing the influence of temperature upon 
the fugacity for a single phase, in the form, 

( 9R Tlnif, \ 

v 9 T / 

= -& 

This equation is in general not true, notwithstanding the fact that we 
may choose arbitrarily the zero of entropy. If for each temperature 
this zero could be chosen arbitrarily it could be so chosen that the equa- 
tion would be true, but as a matter of fact the entropy is in all cases a 
determinate function of the temperature, and the zero chosen for one tem- 
perature must be retained for all. We must conclude, therefore, either 
that the general equation (19) is false, or that entropy is not the capacity 
dimension of heat. To make the latter conclusion would appear too 
arbitrary were it not that other considerations lead also to the suspicion 
that entropy has been too hastily chosen as the capacity in question. In 
fact, the equation, d Q = TdS, for the heat absorbed in a reversible 
process, corresponding to the general equation for change of energy, 
dE — Id H, is the only argument for the consideration of entropy as 
the capacity dimension of heat. This argument would apply equally 
well to any other quantity, h, such that d Q = ± Td h ; in other words, 
such that dh = ± d S. It is interesting, therefore, to determine whether 
there is, in fact, a quantity which fulfils this condition and also the 

If a simple function can be found which satisfies these two require- 
ments it may, I think, be accepted, at least provisionally, as the true 
capacity of heat energy. 

The entropy of every body is a very complex function of its other 
variables, and even the entropy of a perfect gas is represented by the 
complicated equation,* 

S=S f- G P \n^-R\n^. 

* See Clausius, Warmetheorie, I. p. 214, third edition. 


The value of h for a perfect gas may be found from the second of the 
above conditions, equation (21). For a perfect gas, according to the 
definition of fugacity, 

\p = P, and therefore 

, (9RT\u^\ {9RT\nP\ 

h = \~-rr^) P = \--^T-)r RlxlP ' (22) 

We see, therefore, that the value of /* which satisfies the condition of 
equation (21) is expressed by a far simpler function than entropy is. 
Let us see whether this value for the perfect gas is consistent with the 
other condition that, 

dh= ± dS. 

For a perfect gas the following equations for isothermal change are 
familiar : 

dQ Pdv vdP RdP __ 1 _ 

and from equation (22), 

d h = R d In P, hence, for constant temperature, 

dh = — dS, (23) 

and the condition is satisfied. The value R In P satisfies both the above 
conditions for h in the case of a single state, the perfect gas. Moreover, 
every substance is capable of being brought into the state of a perfect 
gas isothermally by evaporation and indefinite expansion. Consequently 
it is easy to show that for any state of a substance either of the two 
conditions will define a value of h which is consistent with the other 
condition. Thus by the first condition, expressed now by equation (23), 
the difference in value of h between two states of a substance is equal to 
the difference in entropy and opposite in sign, that is, 

h, — /?2 == iJ-2 — *^1* 

If we choose as the second state the vapor of the substance at such a 
low pressure, P 2 , that the vapor may be regarded as a perfect gas, 
h 2 = R In P 2 , from equation (22), and the last two equations give, 

h 1 = Ss-Si + BlnP* (24) 

in which *^ 2 represents the entropy of the vapor at pressure P 2 . This 
equation furnishes a complete definition of the value of h for any state. 
Let us see whether this value satisfies the other condition of equation 


Equation (16), namely, 


2 — Oj, 

holds true for the two states which we have just considered, one of 
which is the vapor in the state of a perfect gas at the low pressure P 2 . 
By the aid of equation (24) we may therefore write 



hi-fi In P 2 . 

According to (22) 

and the last two equations give by addition 

\ 9T )r K 

which is equation (21). 

I think, therefore, that we are justified in considering h the true 
capacity dimension of heat, and in considering equation (21) the special 
form of equation (19) applied to heat energy. The replacement of 
entropy in general energy equations by the quantity h will have a 
further advantage on account of the much greater simplicity of the 
latter, the approximate value of which may be in all cases very easily 
determined by assuming that the vapor of the substance in question may 
be regarded as a perfect gas, in which case equation (24) evidently 

h = ^ + E]np, (25) 

where Q is the total heat absorbed in the evaporation of one gram- 
molecule and p is the vapor pressure.* 

We have now obtained equations of the form of (19) for two of the 

* This approximate equation is a special form of a general and rigorously exact 

& = ^ + fllnf, (25a) 

in which i|/ is the escaping tendency of the substance and Q' is the heat absorbed 
when one gram-molecule is allowed to evaporate irreversibly against an infini- 
tesimal vapor pressure. Since this equation will not be used in this paper its 
demonstration may be postponed. 


most important kinds of energy. The fugacity is also known to be a 
function of a third energy-intensity, namely, surface tension. Let us 
consider a drop of liquid containing n gram-molecules with a surface o- 
and a surface tension t. The change in surface of the drop with a 

change in its content expressed in gram-molecules, that is, — — , has been 


called the molecular surface, and we may designate it by s. If the 

quantity dn is taken from the drop and added to a large mass of the 

liquid the process is capable of yielding work. The amount has, I 

think, always hitherto been written equal to tela, the change in surface 

energy. This is not strictly true. The molecular volume in the drop is 

not exactly equal to but always slightly less than the molecular volume 

in the large mass. There is therefore always a small amount of work 

done against the atmosphere, and the total work capable of being done by 

the transference of dn gram-molecules is equal to t d cr + P (d v — d v), 

where dv represents the increase in the volume of the large mass, dv 

the decrease in the volume of the drop. If the transfer be made reversi- 

bly in any way the total amount of work obtained must be equal to the 

above. The transfer may be actually carried out reversibly as follows : 

Let a solvent be chosen in which the liquid in question is so slightly 

soluble that the solution may be regarded as an ideal one. The drop 

and the large mass of liquid will be in equilibrium * with the solution at 

two different osmotic pressures, II and II , respectively. We may now 

take the following steps reversibly: (1) dn gram-molecules of the drop 

dissolve into its saturated solution, (2) the same amount is diluted to the 

osmotic pressure II , and (3) passes out of solution into the large mass. 

The three steps yield the following amounts of work, in which d vj and 

d v' represent the volumes occupied by the amount d n in solution at the 

osmotic pressures II and II, respectively. 

Wi = Udv' - Pdv, 
W 2 = dnRT\n^> 

W 3 = Pdv -Il dv>. 

The sum of these terms, written equal to the amount of work given 
above, gives 

* In order not to affect the surface tension of the drop, it may be separated 
from the solvent by its own vapor and thus pass into solution through the vapor 


P{dv -dv) + Udv'-U dv ' + dnRTln — = 

tda+ P(dv -dr). 
Now from equation (2), II d vj = II d v', 

U^ if/ 

and, as on page 55, 

RTlu^ = t^ = ts. (26) 

This is the general equation connecting fugacity and surface tension at 
constant temperature and pressure. If t is variable we may differentiate, 
\p and s being constant, obtaining 

dR Tlnif/ = sdt, 

or expressing the constancy of T and P, 


C-srf )„...=* (27) 

This equation completely confirms the validity of equation (19) as 
applied to surface energy and corresponds to equations (20) and (21). 
An important form of energy which we have not yet discussed is 
electrical energy, whose dimensions are potential, and quantity of elec- 
tricity. If these be represented by i? and e, respectively, in any case 
where the fugacity is influenced by the electrical potential, we should 
have the equation, 

(-^L.=* (28) 

There are in fact a number of cases in which the potential may be 
shown to have an effect upon the escaping tendency, the most important 
being that in which the potential influences the fugacity of the ions. The 
following equation has been amply proved experimentally, and thermo- 
dynamically is shown to be rigorously exact on the assumption that the 
ions form an ideal solution. 

e 77 = R T In n + K, 

in which tt is the potential at which equilibrium is established between 
an electrode and its ions at the osmotic pressure II, if e is the charge of 
one gram-ion and K is at constant temperature and pressure a character- 
istic constant of the electrode. In other words, II is the osmotic pressure 
of the ions which will be in equilibrium with the electrode when the 



potential ir is established. Since we are discussing an ideal solution this 
osmotic pressure is proportional to the fugacity of the ions. That is, 
from equation (8), \p = p II, and 

€ 77 = R T In ijf - R Tin p + K. 

Differentiating at constant temperature and pressure we obtain the 


( 9RT\nxp \ 

V Sir Jt,p,... 
which is equation (28). 

Equations (20), (21), (27), and (28) comprise all cases in which 
fugacity is known to depend upon the intensity of any form of energy. 
The identity of these equations with equation (19) gives the highest 
degree of probability to the supposition that the latter equation expresses 
an exact law of nature and one possessing such universality as few 
others possess. For this equation expresses the condition for any con- 
ceivable change of state of any simple substance. Moreover, it will be 
shown in the paper which is to follow this, that equation (19) not only 
applies to chemically simple substances but, with a slight generalization 
in the meaning of the symbols which it contains, applies to mixtures as 
well, and further that it applies not merely to physical processes but also 
to all chemical processes,* so that this law becomes the general law of 
physico-chemical change. 

Finally, it will be shown that the adoption of the two functions \p and 
R Tlnif/, which possess such peculiar importance, will remove many 
obstacles in the search for the fundamental principles of energetics, in 
which already so much progress has been made by the work of Helm, of 
Ostwald, and of other investigators. I shall therefore offer in the last 
section of this paper a further explanation of fugacity as a tangible, 
physical quantity. 


The Fugacity of Imperfect Gases. 

The vapor pressure is determined for many substances and capable of 
direct or indirect determination for all. Moreover the fugacity of a sub- 

* In the further extension of this theory, analogy will be seen between the 
conception of fugacity and the driving tendency of chemical reaction as used by 
T. W. Richards (These Proceedings, 35, 471 ; Jour. Phys. Chem., 4, 385 (1900)). 
It is a pleasure to recall how much I owe to the many conversations full of assist- 
ance and encouragement which I had with Professor Richards during the early 
development of the theory of fugacity or escaping tendency. 



stance is the same as that of the vapor in equilibrium with it. It is 
important therefore to know what relation exists in general between thi 
fugacity of any gas or vapor and its pressure. 

Figure 3. 

If a section of the isothermal of any vapor is plotted on the P V dia- 
gram (Figure 3) we obtain a curve such as M M', which, according 
the third law stated in the introduction, approaches asymptotically I 
hyperbola N N', whose equation is, 

P v = RT. 

Let us determine the value of if/ for any point M of the curve. Tl 
variation of if/ with P is given by equation (20), which may be written 
for constant temperature, 

d R T In if/ = v d P. 

Between the two points M and M' we find by integration 


V J M 

I- d p. 

Now if the lines of constant pressure L M N and L' M' N' are drawn, 
I v dP is equal to the area M M' L' L, and this is equal to the area 


L N N' L' minus the area M M' N' N. The former area is equal to 


R Tin—, and if the latter be designated by A we have the equation, 

RT\n^ = RTln^- A. (29) 

Now if the point M' is moved in the direction of greater volume, equa- 
tion (29) holds true continuously, and therefore is true if M' is taken at 
infinite volume. But at infinite volume 

*' = P', 
and therefore 

R T\m}, = R TlnP-A^, (30) 

if A m represents the total area bounded by the line M N and the curves 
M M' and N N', each produced to infinity. This equation may be 

RTln^ = -A a ,OT\*^ = -^ i ,oT $ = Pe = £, (31a) 

where e is the base of natural logarithms. 

The deviation of the fugacity from the gas pressure is, therefore, 
dependent upon the area A^. The case that has been chosen in which 
the curve M M' lies within N N' is of course the common one. For 
gases of the opposite type, hydrogen and helium, the formulae will be, 

R Tln^ = + A„ andi/, = Pe^ (31b) 

We see at once that for all known gases and vapors except hydrogen 
and helium the escaping tendency is less than the gas pressure ; for 
these two, greater. The determination of the value of the fugacity at 
any pressure involves the estimation of the area A v . This must be 
done by integrating the most exact empirical equation of the isotherm of 
a s;as between the pressure in question and the pressure zero. This 
method has the disadvantage of all extrapolation, but the value thus 
obtained may be checked by using a second empirical equation of 
another form and recalculating A^. If the two results coincide the 
value obtained will in all probability be very near the true value of A^. 
In conclusion it may be remarked that equation (29) applies to the 
isothermal of all substances, not merely to gases, and can be frequently 
of use. For example, if it is possible to pass continuously from vapor to 
liquid along an isothermal, it is evident that in passing from a saturated 
vapor to its liquid, 


<// = «//, and P= P' 

in equation (29). Therefore the total area A reckoned algebraically 
must equal zero. That is, the two areas on the two sides of the line of 
constant pressure P must be equal. This is the well-known principle 
of Maxwell. 


(1) The equation of Clausius for vapor pressure is simplified. 

(2) The meaning and utility of a new quantity, the escaping tendency, 
or fugacity, are explained. 

(3) The influence of temperature and pressure upon fugacity is ex- 
pressed in simple equations. 

(4) A simple, general equation, which embraces every possibility of 
the change of state of any simple substance, is proposed. 

(5) This equation rests upon the conception of the intensity and 
capacity dimensions of energy. 

(6) This equation is verified as applied to the influence of pressure on 

(7) This equation is verified as applied to the influence of temperature, 
if a new quantity, instead of entropy, is regarded as the capacity dimen- 
sion of heat. 

(8) This equation is verified for the influence of surface tension. 

(9) This equation is verified for the influence of electrical potential. 

(10) A method is offered by which the fugacity may be found from 
the vapor pressure. 

Proceedings of the American Academy of Arts and Sciences. 
Vox. XXXVII. No. 4. — August, 1901. 


By Edward L. Nichols. 

hsatioss os Light A5i> Heat, mai»e ahtj published wholly oa ra part with Appropriation-* 


By Edward L. Nichols. 

Presented May 8, 1901. Received May 15, 1901. 

The law of radiation has for a long time been considered by physicists 
as a subject of high interest, and numerous investigations looking to the 
establishment of a general relation between radiation and temperature 
have been made both from the theoretical and the experimental stand- 
point. The earliest attempts to determine incandescence in its relation 
to temperature were made with platinum. Draper f in 1847 made 
observations upon a wire of that metal heated by an electric current. 
The temperatures were determined from the expansion of the wire. 
ZolIner$ in 1839 compared the light emitted by incandescent platinum 
with the heat evolved. E. Becquerel,§ who made an extensive study of 
visible radiation from various solids at high temperatures, used thermo- 
elements of platinum and palladium, calibrated by reference to melting 
points with the air thermometer. A partial separation of the rays was 
effected by means of colored screens. 

Becquerel found that opaque bodies, such as lime, magnesia, platinum, 
and carbon, at the same temperature had very nearly equal emissive 
powers, a conclusion vigorously contested by his contemporaries, but ex- 
plained, in the light of later work, by the fact that the -lowing bodies 
were enclosed in a long earthen tube. The conditions for ideal blackness 
were thus approximately fulfilled. He likewise made photometric obser- 
vations upon wires electrically heated and found the' light to increase 
much more rapidly than the emitted heat. 

Although some of Becquerel's results were at fault, particularly his 
estimation of temperature above the melting point of gold, his work is 
especially noteworthy in that he employed many of the methods to which. 

* An investigation carried on in part by means of an appropriation from the 
Rumford Fund. Read at the meeting of the American Association for the Advance- 
ment of Science in New York, June 27, 1900. 

t Draper, Philosophical .Magazine, XXX. 345 (1847). 

| Zollner, Photometrische Untersuchungen (1859). 

§ Becquerel, Annales de Chimie et de Physique, (3), LXYII. 17 (1863). 


iti the hands of later investigators, our knowledge of the laws of incan- 
descence is due. He established the direct proportionality of the loga- 
rithm of the intensity of radiation to the temperature and pointed out the 
possibility of optical pyrometry. 

In 1878 Crova* used the Glan spectrophotometer in the comparison 
of various sources of light, such as candles, gas flames, the lime light, the 
arc light, and sunlight, and proposed au optical method for the measure- 
ment of temperatures. 

In 1879 f I published the results of a series of measurements made in 
this manner upon the visible radiation from platinum at various tempera- 
tures. At that time, the measurement of high temperatures by means 
of thermo-elements, of platinum and platinum-rhodium, or platinum-ind- 
ium, had not been developed, aud j the determination of the temperature 
from the change of resistance of the metal was, as has been previously 
pointed out by Siemens, a matter of great uncertainty on account of the 
varying performance of different samples of platinum. This difficulty, 
which was due to the impurities contained in the metal, has since been 
largely overcome, and platinum thermometry has, through the study of 
Callendar and others, been advanced to the position of au operation of 
precision, but at that time I was forced to content myself in the investi- 
gation just referred to with an expression of temperature of the glowing 
platinum in terms of its increase of length. 

Work upon the incandescence of carbon was first taken up in a serious 
manner after the development of the incandescent lamp. 

Schneebeli,$ in 1884, made some observations upon the total radiation 
and candle power of the Swan lamp. He made no estimation of tem- 

In the same year Schumann § published his very complete spectro- 
photometric comparison of the various incandescent lamps in use in 
Germany. Lucas, || in 1885, heated arc-light carbons in vacuo, estimated 
their temperature from the current employed, and measured the light 
given in carcels. I shall refer to his work in some detail later. 

In 1887 H. F. Weber U began his studies of the spectrum of the in- 

* Crova, Comptes Rendus, LVII. 497 (1878). 

t Nichols, Ueber das von gliihendem Platin ausgestrahlte Licht. Gottingen, 
1879 ; also American Journal of Science, XVIII. 446 (1879). 
t Schneebeli, Wiedemann's Annalen, XXII. 430 (1884). 
§ Schumann, Elektrotechnische Zeitschrift, V. 220 (1884). 
|| Lucas, Comptes Rendus, C. 1451 (1885). 
IT Weber, Wiedemann's Annalen, XXXII. 256 (1887;. 


candescent lamp. He found that the first light to appear was not that of 
the region nearest the red end of the spectrum, but corresponded in wave 
length to the region of maximum lumiuosity, and that at these low tem- 
peratures the spectrum was devoid of color. Stenger* in the same year 
corroborated Weber's observations and offered what has since b< 
received as the proper explanation of the phenomenon. 

In 1889 I published in collaboration with W. S. Franklin f a series of 
spectrometric comparisons of incandescent lamps maintained at various 
degrees of brightness. No attempt was made to determine temperatures. 
In 1891 II. F. Weber t read a paper at the Electrotechnical Congress 
in Frankfurt on the general theory of the glow-lamp. By means of 
numerous measurements through a wide range of incandescence made 
upon lamps with treated and untreated filaments, constants were estab- 
lished for his empirical formula for the relation of radiation and tempera- 

The infra-red spectrum of carbon has, since the appearance of the 
incandescent lamp, likewise been subjected to measurement. Abney and 
Festing § in 1883 published curves for the distribution of energy in the 
spectrum of such lamps from measurements male with the thermopile. 
In 1894 I compared, with the help of the same instrument and a highly 
sensitive galvanometer, the infra-red spectra of lamps with black and gray 
filaments. || 

Of late years attention has been devoted especially to the problem of 
the law of radiation from an ideal black body, and various formulae have 
been proposed by means of which the rise of radiation of any single wave 
length upon the one hand, and of the total radiation on the other, may be 
expressed as a function of the temperature. Interesting as this phase of 
the problem is from the point of view of theoretical physics, it is perhaps 
even more important to know the relation between temperature and 
radiation for actual surfaces. 

Apparatus and Outline of Method. 

I propose in the present paper to describe an attempt to measure the 
temperature of carbon rods rendered incandescent by the passage of an 

* Stenger, Wiedemann's Annalen, XXXII. 271 (1887). 

t Nichols and Franklin, Am. Jour, of Science, XXXVIII. 100 (1880). 

| Weber, Bericht des internationalen Flektroteehniker-congresscs zu Frankfurt 
am Main, p. 49 (1891); also Physical Review, II. 112. 

§ Abney & Festing, Philosophical Magazine, (5) XVI. 224 (1833); also Pro- 
ceedings of the Royal Society, XXXVII. 157 (1884). 

II Nichols, Physical Review, II 260 (1894). 



electric current, and to make spectropliotometric comparisons of the 
visible radiation from their surfaces with the corresponding wave lengths 
m the spectrum of an acetylene flame. 

The carbons used for this purpose were produced by the well-known 
process of squirting a semi-fluid carbonaceous paste through a cylindrical 
opening. They were straight cylindrical rods 10 cm. in length, and 2 mm. 
in diameter. Still larger rods would have been preferable, but I was 
unable to obtain any of greater diameter than the above that were capa- 
ble of withstanding the temperatures to which it was necessary to heat 
thetn. The rods were mounted horizontally in a massive metal box 
40 cm. in length, 20 cm. wide, and 20 cm. in height. This box, which was 
made especially for this investigation, had openings at the ends, through 
which, by means of air-tight plugs, the terminals of the carbon could be 
introduced. Through one of these plugs, likewise, the platinum and 
platinum-rhodium wires of the thermo-element, by means of which the 
temperature measurements were made, entered the box. In one of the 
vertical sides of the box was a row of five circular plate-glass windows, 
which could be removed for cleaning, through which the carbon could be 
seen and the spectropliotometric observations couM be made. Other 
openings in the top of the box and through the opposite sides served to 
connect it with a mercury air pump of the Geissler type and for the 
introduction of manometers for the measurement of pressure. A vertical 
cross-section of this part of the apparatus is shown in Figure 1. Attempts 

7o jnanom&tci- To fiumjo 

Figure 1. 


i i 

to locate, by a variety of methods, the hot junction of the thermo-element, 
by means of which the temperature of the surface of the roils was to be 
measured, in such manner that it would assume the temperature of that 
surface, made it only too clear that herein lay one of the chief difficulties 
of the investigation. It was found that such a junction, however small 
its size, and however carefully it might be brought into contact with the 
surface of the rod, would not take even approximately the temperature of 
that surface ; and recourse, after the failure of numerous other expedients, 
was had to the following plan, which although far from being free from 
objection, was found to be upon the whole the most reliable, and to give, 
when properly carried out, the most definite and satisfactory result. 

By means of a drill made for the purpose from the smallest obtainable 
size of steel sewing-needle, a minute hole was bored radially at a point 
upon the surface of the rod lying within the field of view of the spectro- 
photometer. This hole had an approximate diameter of 0.03 cm. It 
extended to a depth equal to about one half the radius of the rod and was 
conical in form. Platinum and platinum-rhodium wires to he used for 
the thermo-element were drawn to a diameter of 0.0 1G cm., and their 
free ends having been. laid together side by side, were fused in the flame 
of the oxyhydrogen blowpipe so as to form a junction. This junction, 
which after the action of the blowpipe took the shape of a small bead of 
the combined metals, was trimmed down into conical form, until it would 
just enter the hole in the side of the rod, care being taken that the 
entire junction was beneath the surface. The wires leading from this 
junction were next sealed into a glass tube of about 2 mm. bore, through 
the interior of which they were carried from end to end, care being 
taken that they should be nowhere in contact. They were held in place 
by fusing the glass around them at either end of the tube. This tube 
was inserted through an opening in the plug a 
(Figure 1) carrying one terminal of the rod, 
and there made air tight by means of cement. 
One end of the carbon rod was then inserted 
in a clamp attached to the inner face of the 
plu"-, and the wires at a distance of about 
1 cm. from the junction were bent downward 
at right-angles, so as to bring the junction 
into position for insertion into the hole in the 
rod, and to hold it there when inserted by 
the slight but sufficient spring-action of the 

wires themselves. This arrangement of the junction and rod is indicated 
in Figure 2. 

Figure 2. 


The introduction of the thermo-element having been successfully car- 
ried out by the method just described, it was possible to insert the plug, 
carrying the rod and thermo-junction with it, into the end of the box 
and to secure it in place ; after which the free terminal of the rod was 
introduced between the jaws of a strong clip attached to the opposite 
plug (b, Figure 1). This operation had to be performed through the open 
windows in the side of the box. These were then screwed rightly iuto 
place, and the box was ready for the exhaustion of the air. 

This method of measuring the temperature of the surface, to be suc- 
cessful, involved the fulfilling of several rather difficult conditions and 
the application of an important correction. To bore into the material of 
a carbon rod carrying a current in the manner described, necessarily dis- 
turbs more or less the flow of the current ; and the changes of resistance 
thus introduced are likely to bring about decided changes of tempera- 
ture in that neighborhood. In some instances this became obvious when 
the rod was heated, the temperature being higher near the hole than else- 
where. Indeed, it was often possible to note this effect with the eye on 
account of the increased incandescence of the region in question. In all 
such cases the mounting was rejected. It was found possible, however, 
to so nearly compensate for this loss of carbon by the introduction of the 
platinum junction that no difference in the incandescence of the surface 
could be detected by the closest observation ; and since differences of 
temperature which cannot be detected by the eye will be negligible in 
spectrophotometric work, this was taken as the criterion of a satisfactory 
mounting of the thermo-junction. Measurements were attempted only 
when this condition was fulfilled. It is likewise obvious that there is 
danger from the contact of the two wires of the thermo-junction with the 
sides of the hole in the rod. A branch circuit for the passage of the 
current is thus formed which includes the galvanometer coils, thus im- 
perilling the integrity of the readings of the electromotive force. This 
could be obviated only by having the wires touch the rod at points in an 
equipotential surface, and the fulfilment of this condition was determined 
by the reversal of the current through the rod and the absence of any 
effect of such reversal upon the galvanometer. 

Another and more serious objection to the method, and one which 
could only be met by the introduction of a correction, lay in the fact that 
even with the smallest wires which could be used for a thermo-element a 
certain amount of heat would be carried away by conduction through the 
metal ; so that the junction would never reach the full temperature of 
the surfaces with which it was in contact. I was at first inclined to think 




that this correction would be a small one, but attempts to measure in a 
similar manner the temperature of the acetylene flame indicated that the 
loss of heat from this source was by no means to be neglected. These 
attempts are described in a subsequent section of this paper. 

The numerical value of this correction was accordingly determined 
by direct experiment in the following manner. Thermo-elements 
drawn from the same pieces of wire but differing considerably in 
diameter were prepared. These were inserted two at a time in holes 
on opposite sides of a carbon rod and the rod was brought to incandes- 
cence by means of the current. The temperatures reached by these 
junctions were compared by means of the potentiometer, and a curve 
was plotted showing the relation between the cross-section of the wire 
in the thermo-element and the temperature of the junction. This curve, 
extended in the direction of decreasing cross-section, served to indicate 




00 1 

oo J 

oo * 


Relative Cross-sections. 
Figure 3. 

with at least a fair degree of accuracy the temperature which would 
have been reached by a thermo-element of zero cross-section placed in 
contact with the surface to be measured. The difference between this 
temperature and that reached by a junction of any desired size gave the 
correction which was to be applied. The correction, as will be seen by 
inspection of the curve, Figure 3, is a very large one, amounting, even in 
the case of the smallest wires which it was found practicable to use, to 


about 85°. The result of the calibration agreed, however, so well with 
similar experiments made by placing thermo-j unctions of various sizes in 
the non luminous outer envelopes of the acetylene flame, of the ordinary 
gas flame, and of the flame of the candle, that I feel warranted in placing 
much dependence upon them. 

The correction is not of the same size in the various cases, but the 
differences are such as one would expect from the nature of the flames. 

This method of correcting for the loss of heat in a thermo-junction 
was first employed by Waggener * in his investigation of the temperature 
of the flame of the Bunsen burner. I became acquainted with his 
research only after the completion of my experiments. 

Calibration of the Thermo-Elements. 

All our estimates of very high temperatures may be said to rest in 
one way or another upon extrapolation. Tne upper limit of usefulness 
of the air thermometer has been found to lie in the neighborhood of 
1.300.° At this temperature Erhardt and Schertel, t in their admirable 
but little known research upon the melting-points of alloys of silver, 
gold, and platinum, were obliged to abandon direct determination ; and, 
at about the same temperature, Holborn and Wien and Holborn and 
Day I in their latest studies upon thermo-electric thermometry found that 
the indications of the air thermometer, even when constructed of the 
most refractory of modern porcelain, began to be erratic. We have, it 
is true, the investigations of Violle § upon the melting-points of the 
metals of the platinum group; but these, it must not be forgotten, are 
based upon an assumed value for the specific heat, and this assumption is 
equivalent to the extrapolation of the curve of the variation of the 
specific heat with temperature. The observed values, by means of 
which this value was determined, all lie far below those of the melting- 
points of the metals in question. It is necessary, therefore, in spite of 
the accumulation of indirect evidence of their approximate accuracy, to 
hold in reserve the assignment of absolute values of these melting-points 
until by some means as yet unthought of we shall be able to obtain 
direct experimental data. In the meantime, they afford us the best 
present available basis for a temporary scale, our confidence in the 

* Waggener, Wiedemann's Annalen, LVIII. 579 (1896). 

t Erhardt and Schertel, Jahrbuch fur das Hiittenwesen in Sachsen, 1879, p. 

\ Holborn and Day, American Journal of Science, VIII. 1G5 (1899). 

§ Violle, Comptes Rend us, LXXXIX 702, 1879. 


approximate accuracy of which must rest upon the fact that the melting- 
points for palladium, platinum, etc., as given by Violle arc found to lie 
upon what may reasonably be supposed to be an extension of the curves 
experimentally determined for lower temperatures by means of the air 
thermometer. As for the various formulae for the variation of electro- 
motive forces of thermo-elemeuts with the temperature, we must not lo 
si'dit of the fact that they are simply analytical expressions for experi- 
mentally determined relations, and that the extension of them to temper- 
atures lying far beyond the experimental range is not to be regarded as 
more trustworthy than the extention of a curve by graphical methods. 

Under these circumstances I decided to content myself with the pro- 
visional acceptance of the following values for the melting-points 
gold, palladium, and platinum, namely : — 

Gold, 1075° C 

Palladium, 1500° C 

Platinum, 1775°C, 

and to ascertain as accurately as possible the electromotive force given 
by the thermo-elements used at these points. It was thought that b\ 
drawing a curve through them, and reading intermediate temperatures 
from this' curve, the values obtained would be as close as our present 
knowledge of the subject will admit. The platinum, platinum-rhodium 
wire used for my elements was obtained, as has already been state I. 
from Heraeus in Hanau and was supposed to be of the same stock as 
that employed by Ilolboru and Wien. The fact that the electromotive 
force given by these thermo-elements when exposed to the temperature 
of melting platinum agreed very closely indeed with that obtained 1»\ 
extrapolation of their data seems to indicate that the metals were identi- 
cal with those used by them. 

Exhaustive studies at the hands of Le Chatelier,* of Barus,t and ol 
Holborn and Wien. t and others have led to the conclusion that whenevei 
thermo-elements consisting of platinum on the one hand, and ol the 
alloys of that metal with iridium, rhodium, or any other metals of 
platinum group on the other, are to be used in the measurements of 

* Le Chatelier, Comptes Rendus. CII. (1860) 819; Journal de IV 
VI. 26 (1887) ; also Mesure des Temperatures fclevees [Paris, 1000), Chapter VI. 

t Barus, Bulletin of the U. S. Geological Survey No. 54 ; also American -lour 
nal of Science, XLVIII. 336. 

t Holborn and Wien, Wiedemann's Annalen, XLVIT. 107 (1892); LV1 

560 (1895). 




high temperatures, it is necessary to make a thorough calibration of the 
individual thermo-elements involved, or at least of the set of elements 
manufactured from any given sample of metal. How important it is to 
perform such a calibration for one's self may be seen from the fact that 
Ilolman, Lawrence, and Barr* obtained an electromotive force of .0303 
volts from a platinum, platinum-rhodium (10%) element at the tempera- 
ture of melting platinum, whereas a similar element constructed of wire 
from Heraeus gave in the hands of the present writer .0182 volts at the 
same temperature. 

Numerous more or less complicated methods of calibration involving 
the use of various forms of the gas thermometer have been proposed, 
the carrying out of which involves the use of special apparatus which 
is difficult of construction and laborious in operation. Fortunately it was 
possible in the present investigation to substitute for these a new and 
easy method in which the acetylene flame itself was the source of heat. 
This method t possesses the advantage of extreme simplicity, and it 
affords indications the accuracy of which leaves little to be desired. 

The acetylene flame em pi »yed was of the usual flat form produced by the 
union of two impinging jets. There are three distinct stages observable 
in the form of such a flame, depending upon the pressure at which the gas 
is supplied to the burner. In the first, we have two separate cylindrical 
jets of small size (Figure 4 a), which, with increasing gas pressure meet 
without uniting, each being deflected, by impinging upon the other, into 
a vertical plane (Figure 4 b). At still higher pressures the actual union 
of the two jets takes place, giving the flame the structure shown in (Fig- 

* Holman, Lawrence, and Barr, J. Am Acad, of Arts and Sciences (1895), 
p. 218. 

t This method of calibration has been separately described in a contribution to 
the Lorentz Jubilee Volume. The Ha cue, 1900. 



ure 4 c), in which the two cylindrical jets of gas in the process of combus- 
tion unite to form a single flat vein or envelope which constitutes the 
luminous portion of the flame. When this third stage is readied, there 
is oreat stability of form and position. Such a flame responds with a 
sharp lateral motion to air waves such as are produced by the slamming 
of a door, but is comparatively unaffected by slight drafts. Even in a 
room not essentially free from air currents the lateral motions of the 
flame, which may be accurately observed by throwing an enlarged 
ima^e of it, viewed edgewise, upon a screen, rarely amount to more 
than .1 mm., and in an especially protected place, these lateral move- 
ments become entirely imperceptible. The temperature gradient in the 
layer of air bordering upon the luminous envelope of such a flame is 
very steep, but it is capable of definite deter- 
mination by exploration with suitable thermo- 
elements, and so long as the flame remains 
undisturbed by lateral drafts its stability is 


The burner used is of a well-known form 
(Figure 5), and is made from a single block of 
steatite. It is mounted upon a horizontal bar 
of steel (Figure G), along which it may be Figure 5. 

moved by means of a micrometer screw. 

The bar is set up in an inner room without windows, being opposite a 
circular opening in the wall through which the flame may be observed 
from without. In this opening is placed the lens of a micro-camera, 


Figure G. 

upon the ground-glass screen of which instrument, at a distance of abut 
two meters, an enlarged image of the flame is focussed. The platinum 
and platinum-rhodium wires to be tested are drawn down to a 



Figure 7. 

size (diameter about 0.01 cm.), and a thermo-element is formed by cut- 
ting pieces of the platinum wire, and of the wire of the alloy to be used, 
about 70 cm. in length, and binding these to the opposite faces of a 
rectangular block of wood about 1 cm. in thickness. Beyond this block 

the wires project about o cm. They are bent 
toward each other until the free ends are in 
contact, forming a V, and these ends are then 
fused in the oxyhydrogen flame, forming a 
junction, which is subsequently trimmed down 
to the form shown in Figure 7. The apex of 
the V is cut away until the arch of fused metal 
joining the two wires is considerably less in 
thickness than the diameter of the wires them- 
selves, the face of the junction forming a smooth plane surface. 

The formation of such a junction becomes, with practice, a simple 
matter, and can be performed, as it is necessary to do after each obser- 
vation, in a few moments. The junction is rigidly mounted upon the 
steel bar with the plane passing through the wires of the V vertical and 
the plane surface of the metal which forms the face of the junction 
parallel to the flat face of the acetylene flame. To the free ends of the 
wires are soldered the copper terminals of the galvanometer circuit, and 
the junctions are placed in a bath of meking ice. The support carrying 
the thermo-element is mounted in such a position as to bring the face 
of the hot junction as nearly as possible into the centre of the field of 
view of the camera, where it is clearly visible under the illumination of 
the acetylene flame, which should, at the beginning of the operation, be 
about 1 cm. from the junction. The micrometer screw, by means of 
which the flame is moved along the bar, is operated by means of a long 
handle with a universal joint; so that the flame can be shifted by an 
observer sitting opposite the ground-glass screen. For the measure- 
ment of the electromotive forces produced by the heating of the junction 
a potentiometer of the usual form is used. The metals the melting 
temperatures of which are to form points upon the calibration curve, are 
worked into thin foil, and from this foil strips about .03 cm. in width are 
out. Such a strip is looped into the angle of the V and drawn snugly into 
place, the free ends being cut away until they project only about 1 mm. 
beyond the face of the junction. To hold this minute loop of metal 
in its place, it is only necessary to press the foil carefully together 
arouud the junction. The thermo-junction carrying the loop having 
been mounted, in the manner described, in the focus of the camera, 


will be clearly seen upon the ground-glass screen, the ends of the loop 
of metal projecting towards the flame. 

The determination of the electromotive force corresponding to the 
melting-point is made as follows. The observer seats himself in a 
position where he can watch closely the image of the flame and of the 
thermo-element and moves the former gradually toward the junction, 
balancing the potentiometer approximately from time to time as the 
electromotive force rises with the increasing temperature. 

At a definite distance from the luminous envelope of the flame, which 
distance depends upon the character of the metal under investigation, 
the projecting ends of the loop will be seen to melt. So quiet is the 
flame, and so well fixed the temperature gradient from its surface out- 
ward when a proper burner is used, and when the flame is placed in a 
locality reasonably free from air currents, that the fusion of the succes- 
sive portions of the metal loop may be brought about from the end in- 
ward with the greatest nicety; and the electromotive force may be 
determined at each stage until the fusion has progressed to the plane 
coinciding with the face of the junction. Even then, in many cases, 
those portions of the loop of metal which lie within the angle of the 
junction will remain unfused, although their distance from the melted 
portion of the loop is only a fraction of a millimeter. 

The delicacy of this operation under favorable conditions is very great, 
and the agreement of the successive readings of the melting-points of a 
fiven sample of metal is excellent. It is desirable to make a series of 
readings, leading up to the true melting-point, for the reason that when 
the fusion of the metal loop has progressed to that portion which lies in 
contact with the platinum, an alloy is almost immediately formed bet urn 
the fused metal and the junction itself, which affects the thermo-electric 
indications of the couple. For this reason it is not possible to get con- 
sistent readings by repeating observations with a given junction. The 
proper procedure is to cut the wires back 2 or 3 mm. from the apex of 
the V after each set of readings, ami to make a new junction of tin; proper 
form from the free ends thus produced. This requires but little time 
after the operator has gained a reasonable degree of familiarity with the 

When the metal, the melting-point of which is desired, is platinum 
itself, the platinum wire of the junction begins to fuse at the same time 
as the loop, the platinum rhodium or platinum-iridium side remaining 
unmelted. The precise point at which this fusion of the platinum occurs 
is, however, quite as definite as in the case of metals of lower meltiDg 



temperature. This method has the advantage of avoiding the use of the 
air thermometer and of furnaces in which fusion of the metals takes 
place. The amount of metal which it is necessary to melt is almost 
infinitesimal. The loops used in each observation weigh only a fraction 
of a milligram, and the operation may be repeated time after time at the 
will of the observer with the greatest ease. On the other hand it should 
be noted that the method is applicable only to such metals as will fuse 
before oxidation in the hot layers of the acetylene flame. It is not prac- 
ticable with magnesium, aluminium, zinc, or iron, since these oxidize 
under the conditions of the experiment instead of fusing. For ouch of 
the metals of the platinum group as have melting-points below that of the 
junction itself, and for gold, silver, and copper, the method is a convenient 
one, and its accuracy is, I believe, fully equal to that of any other method 
which has thus far been employed. To guard against the deleterious 
influence upon the thermo-junction of the vapors of the flame, it is impor- 
tant to bring the latter up gradually by the slow action of the micrometer 
screw in the manner which I have already described. The atmosphere 
with which the junction is surrounded under these conditions contains an 







*r * 



dp / 
s f 







00 10 

ooo 1 *■ 



Figure 8. 


excess of oxygen, and even where the metal to be melted is platinum 
itself, fusion occurs before the luminous portion of the flame, the action 
of which upon the thermo-electric properties of the junction is to be 
feared, has been reached. It is well-known that a junction, the perform- 
ance of which has been vitiated by exposure to the vapors of a thane or 
furnace, can be restored to its original condition by immersion in an 
oxydizing flame. In this method of calibration the junction is continually 
subject to such oxidation as is necessary to preserve it. Thus one of the 
sources of error which it has been found most difficult to guard against 
in the use of the furnace is altogether avoided. 

Figure 8 contains the calibration curve of the thermo-elements used in 
this investigation, and likewise, for purpose of comparison, a curve repro- 
duced from Waggener's paper and extrapolated by him from data given 
by Holborn and Wien. It will be seen that while the curves are not 
identical they are of the same character, and that the differences are not 
greater than experience would lead us to expect in the case of different 
thermo-elements, even where these are from metals of the same manufac- 
ture. It is not a question of absolute electro-motive forces, but of the 
form of the curves, since what we need is a criterion by means of which 
to determine whether temperature readings based upon Violle's values for 
palladium and platinum are in reasonable accord with those obtained by 
the extension of the curve of Holborn and Wien. 

The Spectrophotometer . 

The spectrophotometer used was a copy of the instrument designed 
by Lummer and Brodhun for the Imperial Institute in Charlotteuburg. 
It consists of a one-prism spectroscope with two collimator tubes, placed 
at right-angles to each other, as shown in Figure 9. Each of these tubes 
carries a slit the width of which is regulated by means of an accurate 
micrometer screw with a drum head divided into one hundred parts. By 
estimating tenths of a scale division, the width of the slits could be esti- 
mated to one one-thousandth of a revolution. 

The essential feature of this photometer consists in the Lummer-Brod- 
hun prism D, placed between the objective lenses of the two collimators, 
and the dispersing prism in such a position that the beam of light from 
one of the tubes is transmitted directly to the latter, while that from the 
other tube is bent to 90° by total reflection. The instrument was set up 
with collimator A in such a position that a portion of the surface of the 
incandescent rod lying nearest to the point at which the thermo-eleinent 
had been inserted formed a field of illumination for the slit at a distance 



of about 25 cm. 





The region under observation was limited by means of 
a vertical diaphragm d, 5 mm. in width, which was 
mounted in a tube in front of a window of the metal 
vacuum box. The comparison source was the spec- 
trum of the brightest part of an acetylene flame set 
up in the axis of the other collimator at a corre- 
sponding distance, and viewed through a circular 
aperture c, 5 mm. in diameter, cut in a metal screen 
interposed between the flame and the slit and as 
near the former as practicable. 

The acetylene flame was adopted as a comparison 

standard for the fol- 






the less refrangible 

lowing reasons : — 
1. It possesses 
a continuous spec- 
trum, brighter in 
regions than that of 


Figure 9. 

any other controllable source of light. 

2. The radiating material is finely di- 
vided carbon, presumably of a character 
not unlike that of the surface of the 
untreated rod. 

3. The acetylene fl ime is the result of the combustion of a definite 
fuel (C 2 rl 2 ) burning under reasonably constant conditions. It is prefer- 
able in this regard to any of the ordinary gas or candle flames in which 
the fuel is of an undetermined and more or less variable character. 

4. When supplied with gas under constant pressure, an acetylene 
flame of the type used in these experiments, that, namely, obtained by 
means of a burner composed of a single block of steatite, is more nearly 
constaut in its intensity and color than any other fkime with which I am 
acquainted, with the exception of that of the Hefner lamp. It is indeed 
questionable whether the latter is superior to acetylene in this respect, 
and its comparative weakness in the blue and violet renders it very un- 
desirable as a comparison source in spectrophotometry. 

Determination of the Temperature of the Acetylene Flame* 
Concerning the temperature of the acetylene flame, varying and in- 
compatible statements are in existence. The temperature of combustion 

* The results of these experiments on the temperature of the comparison flame 
were separately communicated to the American Physical Society on February 24, 
1900, and were published in the Physical Review, X. 234. 


of this gas, according to Le Chatelier,* would be, when burned in air, 
2100° to 2420 . Measurements with Le Chatelier's pyrometer, on the 
other hand, made by V. B. Lewes, f give temperatures lower than those 
of ordinary gas flames. Lewes found for the obscure zone 459,° for the 
edge of the luminous zone 1411,° and for the region near the summit of 
the luminous zone 1517°. Smithells, $ upon the appearance of the data 
given by Lewes, described a series of experiments for the purpose of 
showing that the temperature of the flame reaches, in point of fact, very 
much higher values than those given by that author, and that in many 
portions it is higher than the melting point of platinum. 

It can be easily shown by inserting wires of platinum into the flat 
acetylene flame obtained from any one of the forms of burner usually 
employed, that while the thicker wires remain unmelted, those of very 
small diameter are readily fused. I found, for example, that a wire 
having a diameter of 0.0082 cm. became fused at the end with the for- 
mation of a distinct globule, before the metal had penetrated the outer 
luminous layer of the flame, whereas wires of 0.01 cm. or of larger 
diameter remained unmelted. The experiments of Waggener § show 
that there are portions of the flame of the Bunsen burner in which it is 
possible to melt platinum, while MacCrae, || working with a platinum- 
rhodium element, found for the hottest region in the Bunsen flame 1725°. 
It will be seen from the experiments to be described in this paper, that 
MacCrae's determination, which was made with wires having a diameter 
of 0.02 cm., is not incompatible with the observations of Waggener and 
others. Smithells, in the paper just cited, describes the melting of 
platinum wires having a diameter of 0.01 cm., in various parts of the 
outer sheath of a flat flame of illuminating gas. Pellissier, If in com- 
menting upon Lewes's measurements, refers to experiments in which 
minute wires of platinum, made by Wollaston's method of silver 
plating, drawing, and subsequent dissolving of the silver coating, when 
thrust into the flame of a candle, melted instantly. I have not been able 
to find other printed reference to these observations and do not know 
with whom they originated. An attempt to repeat the experiment with 
a Wollaston wire having a diameter of 0.0011 cm. resulted in the ready 

* Le Chatelier, Comptes Rendus CXXI. 1144 (1895). 

t Lewes, Chem. News, LXXI. 181 (1895). 

\ Smithells, Journal of the Chemical Society, LXIX. 1050 (1895). 

§ Waggener, 1. c. 

|| MacCrae, Wiedemann's Annalen, LV. 97. 

If Pellissier, L'ftclairage a l'acetylene (Paris, 1897), p. 186. 



fusion of the wire by the flame. An examination of the remaining 
portions under the microscope showed that the metal had been melted 
down into clean, well-rounded beads, and had not been consumed by 
oxidation or any other chemical reaction. 

Smithells's contention that the temperature of flames cannot be 
obtained directly from the indications of a thermo-element because of 
the loss of heat by conduction and by dispersion from the surface of the 
latter, so that the portions submerged in the flame never arrive at the 
temperature of the surrounding gases, is well founded. Lewes and 
likewise Waggener recognized this fact, and in their measurements 
made use of wires of different sizes. 

The apparatus which I employed for the determination of the temper- 
ature of the acetylene flame has already been described (see Figure 6). 
The method was similar to that used in the calibration of the thermo- 
elements. The electromotive force of the elements, as these were 
gradually brought into the flame, was measured by means of the 
potentiometer previously employed in the calibration of the thermo- 
elements and subsequently in the determination of the temperature 
of the carbon rods. It consisted of a sensitive galvanometer of the 
d'Arsonval type and au accurately adjusted resistance box containing 
coils ranging from 50,000 ohms to 1 ohm. A large Clark cell of the 
old Feussner type was mounted in series with the resistance box. The 

thermo-element, the galvan- 
ometer, and a subsidiary re- 
sistance of 10,000 ohms were 
looped around a portion of 
the resistance box, the ratios 
being varied until complete 
balance was secured. The 
electrical connections are 
shown in Figure 10. The 
type of standard cell selected 
for this work is subject to 
considerable errors from diffu- 
sion lag. It has, however, the 
advantage of being capable 
of furnishing a much larger 
amount of current than the small types of cell, in which diffusion lag 
is avoided, without appreciable loss of electromotive force. Two of 
these cells were placed side by side in a thick-walled inner room which 



110,000 OHM8. 


Figure 10. 



had been constructed for the purpose of securing uniform temperature 
for the standard clock of the physical laboratory, and other similar 
apparatus. The range of temperature in this room fluctuated through- 
out the entire investigation be- 
tween 18°C. and 19°C. The 
range was so small and the 
variations occurred so gradu- 
ally that no changes of electro- 
motive force of a size which 
it was necessary to consider in 
these measurements could have 
arisen other than those included 
in the usual correction for 

The two cells were compared 
with each other from time to 
time by setting them in opposi- 
tion to one another in circuit 
with a sensitive galvanometer 
and noting the deflection pro- 
duced. It was found that 
although one of them was sup- 
plying current to the 100,000 
ohm circuit of the potentiome- 
ter, during the times when it 
was necessary to close the key 
of that circuit, the difference 
of electromotive force between 
the used and unused cell was 
always very small, never more 
than a few hundred thousandths 
of a volt. At the end of the 
entire set of measurements, the 
difference was 0.00006 volts. 
The absolute electromotive 

force of these cells was checked by comparison with Clark cells of the 
II form and of the test-tube form, constructed in this department in 1898. 
As a result of these comparisons it was found that the electromotive 
force of the cell used in the potentiometer might be taken at 1.430 volts 
at 18.° 






11/ ^ 


iff ' 






6 mm 

4 mm 

Figure 11. 



The wires selected for the four junctions to be used in the experiment 
upon the acetylene flame were measured under a microscope with 
micrometer stage. Their diameters were as follows : — 

Junction I. 
" II. 
" III. 

" IV. 

Diameter 0.0199G cm. 
" 0.01598 cm. 
" 0.01089 cm. 
" 0.00821 cm. 

Readings were first made with junction I. (diameter 0.01996 cm.). 
The flame was set at a distance of 6 mm. from the face of the junction, 
and the potentiometer was balanced. The flame was then moved step- 
wise nearer and nearer, and the potentiometer rebalanced at each step 
until the face of the junction coincided with the edge of the luminous 
mantle at a point just above the apex of the inner nonduminous zone. 

The rise of temperature indicated by the potentiometer readings is 
shown in curve a (Fig. 11), the data for which as well as for the other 
curves in that figure are contained in Table II. 

Temperatures indicated by thermo-junctions I., II., III., and IV. at various 


Junction I. 


unction II. 

Junction III. 

Junction IV. 












. . . 

5.42 mm. 


4.63 mm. 








4.82 mm. 


4.11 mm. 








3.21 mm. 


2.55 mm. 








2.03 mm. 


2.12 mm. 








1.50 mm. 


1.86 mm. 








118 mm. 


1.70 mm. 








0.894 mm. 


1.54 mm. 








0.566 mm. 


1.30 mm. 





0.238 mm. 


1.025 mm. 





0.00 mm. 
- 0.29 mm. 


0.780 mm. 
0.300 mm. 



The iucrease of temperature as the flame approaches the junction is 
gradual at first: but at a distance of about 0.4 cm. from the median 
plane, the curve suddenly becomes steep. It is probable that this 
distance measures the thickness of the layer of non-luminous gas which 
surrounds the visible flame. Outside of this region, the junction is 
heated almost altogether by radiation. As soon as it penetrates the 
column of moving gas, however, heat is brought to it principally by 
convection. Before the surface of the luminous mantle is reached the 
curve shows indications of approaching a maximum. 

Upon pushing the flame still nearer to the junction so that the latter 
penetrated the luminous region, an accumulation of lampblack began to 
form upon the wire, with fall of temperature ; a process so rapid that at 
the end of two minutes a button of carbon several millimeters in diameter 
is formed. This is finally torn loose from the wire by its own weight; 
whereupon the deposition of a new mass begins. I attempted by watch- 
ing the breaking away of the carbon from the wire, which occurred at 
regular intervals, to determine the temperature of the wire before the 
coating of carbon had begun to show itself again. The highest temper- 
ature which it was possible to observe in this way was nearly one hundred 
decrees below that in the luminous layer, and it was obvious from the 
movement of the galvanometer needle that the junction was being rapidly 
cooled by the deposition. 

Junction II. (diameter 0.01598 cm.) was now substituted for Junction 
I., and a similar set of readings were made. This junction, as had been 
anticipated, showed higher temperatures. It was found possible, owing 
to the small diameter and consequently high temperature of the wire, to 
penetrate further into the flame before the deposition of carbon began, 
so that measurements with the junction actually within the luminous 
layer could be made. The general form of the curve, as will be seen by 
inspection of the figure (curve b) is the same as that obtained with Junc- 
tion I. After penetrating the luminous mantle to a small fraction of a 
millimeter, carbon began to gather upon this junction likewise, wilh 
lowering of temperature, as in the case of Junction I. The attempt to 
read temperatures immediately after the dropping of the accumulated 
carbon showed that the highest temperature which could thus be ob- 
served was again about one hundred degrees below the temperature of 
the luminous mantle. It was clear in this case, as before, from the rapid 
fall of temperature already going on, that this reading has no significance. 

Similar readings with Junction III. (diameter 0.0108 cm.) gave a third 
curve of the same type as those plotted from the reading made with I. 


and II., but the temperatures were higher throughout. With this junc- 
tion it was found possible to penetrate to the centre of the flame without 
the deposition of carbon, the temperature of the wire being apparently 
too high to permit the formation of soot. Upon pushing through the 
median plane of the flame to the second luminous mautle, the junction 
was melted. This result was not unexpected, since the temperature of 
the junction at the first luminous mantle reached 1750°, so that a rise of 
twenty-five degrees of temperature would suffice to produce fusion. The 
wire when pushed through the flame in the manner just described is 
heated for greater and greater distances back from the junction until the 
losses of heat at the junction are sufficiently diminished to raise the tips 
of the wires to the melting-point. 

With Junction IV. (diameter 0.0082 cm.), a fourth curve, similar iu 
form to the preceding ones and with still higher temperatures, was ob- 
tained. This junction was fused at a distance of 0.075 cm. from the 
core of the flame, and of 0.037 cm. from the edge of the first luminous 
mantle. It was easy to observe in the enlarged image upon the plate of 
the microcamera the melting away of the platinum wire, while the 
platinum-rhodium alloy was still unaffected, and while contact was still 
unbroken. A satisfactory observation of the electromotive force of the 
thermoelement at the melting-point of platinum was thus obtained. This 
reading (0.018236 volts) differs from the value found in my calibration 
of the thermo-junctions used in this investigation (0.0182G2 volts) by a 
quantity of (0.000026 volts) less than the errors due to changes in the 
electromotive force of the standard cell. If the latter reading be taken 
to correspond to 1775°, the former indicates 1773°. 

Beyond this point, it was impossible to make direct observations of 
temperature ; but the form of this and the preceding curves were so 
closely allied that I felt no hesitation in extending the curve d to the 
core of the flame. This has been done by means of dotted lines in the 
figure. Curves a and b have been extended in the same manner. In 
order to form an estimate of the temperature which would have been 
reached by a thermo- junction of negligible cross-section, provided such a 
junction could have been obtained which was capable of registering tem- 
peratures above that of the melting-point of platinum, the ordinates of the 
four curves, a, b, c, and d were taken for the core of the flame, for the 
plane of the luminous mantle, for a plane distant 0.07 cm. from the core, 
and for a plane 0.10 cm. from the core. These readings were plotted 
and curves were drawn through them as shown in Figure 12; relative 
cross-sections of the wires being taken as abscissae, the temperatures as 









100 200 300 

FlGDRE 12. 


ordinates. If these curves could be extended to the Hue representing zero 
cross-section, the temperatures indicated by the points in which each of 
them cuts that line would give the temperature of the portion of the 
flame to which the curve corresponds. There is a considerable element 
of uncertainty in extrapolation even over so short a range as this ; but it 
is obvious from the character of the curves lying within the limits of 
observation, that each of them trends upward, and it seems highly prob- 
able that they all meet the line of zero cross-section at a temperature not 
far from 1900°. The fact that the curves cut this line at nearly the 
same temperature would seem to indicate that the distribution of tempera- 
tures from the centre of the flame outward for a distance of about 1 mm. 
is a nearly uniform one. 

It would perhaps be unwise to attempt to draw any more definite con- 
clusion from the probable trend of these curves; but I have ventured to 
extend them in the manner shown in the figure, so that the curve for the 
region 1 mm. from the centre of the flame reaches the zero of abscissae 
about twenty degrees above that for the centre of the flume, i. e. at 1920°, 
and the. intermediate curves at temperatures lying between them. I 
regard this as an extreme treatment of the case, and allude to it only to 
indicate that, in accordance with common belief, the highest temperature 


may be found in the outer non-luminous layer of the flame, but that it 

is unlikely that the difference amounts to more than twenty degrees. 

The point of intersection referred to above lies nearly one hundred 

degrees above the highest temperature recorded by even the smallest 

of the thermo-elements, and it is safe to infer that nearly all previous 

attempts at the measurement of flame temperatures must, for lack of 

correction of the error, due to loss of heat through the wire, be regarded 

as much too low. The junction IV. is, so far as I am aware, the smallest 

in cross-section that has been used in such work. With larger wires, 

the correction for loss of heat would be even greater, except in case3 

where, as in the observations made by Smithells, and by Waggener, the 

precaution was taken to immerse an extended portion of the wires within 

the flame. 

Temperature of Other Flames. 

For the purpose of comparison, I measured in a manner analogous to 
that just described, the temperature of the luminous flame of ordinary 
illuminating gas and the flame of a candle. The gas flame employed 
for this purpose was obtained from a lava tip rated at one cubic foot and 
giving a Hat flame of the usual form. The image of this flame, when 

viewed upon the ground-glass screen of my 
camera, was found to be comparatively ill- 
defined and unsteady ; but although the outlines 
of the luminous sheath were much less clearly 
marked than in the case of the acetylene flame, 
they were discernible. Owing to the continual 
motion of the flame, due to the small velocity 
of the gas i-suing from the jet, no attempts 
were made to plot curves of temperatures outside 

the flame. All readings were made with the 
Figure 13. . . , . 

junction as nearly as possible in contact with 

the outer surface of the luminous sheath, at a point in the brightest por- 
tion of the flame. This position is approximately indicated by the letter 
x in Figure 13. The four junctions already described were mounted, 
one after another, in such a position that the flame could be moved up 
until they came into contact with the sheath at the point indicated. The 
temperatures of the junctions when in that position are given in tic 
following table : — 


Junction I. 


Junction III. 








These values having been plotted with relative cross-sections of the 
ires as abscissae, and temperatures as ordinates, were found to lie 




n \ 









— ^ 

100 200 300 400 

cross-section of wire 

Figure 14. 

upon a smooth curve (g) as shown in Figure 14. This curve, when ex- 
tended to the line corresponding to zero cross-section, gave for the tem- 
perature of the flame 1780°, a temperature sufficient to account for the 
success of Smithells's experiment, already described, in which platinum 
wires of small diameter were melted in the outer sheath of such a flame. 
I found it easy, by holding a wire of the size used in junction IV. in a 
plane parallel to that of the flame, and moving it gradually toward the 
latter to verify his statement. The wire was readily melted. 

It was not thought necessary to make further experiments upon this 
flame. The region selected was, so far as one could judge from the 
brightness of the luminous sheath, the hottest portion of flame. My 
measurements upon this region would lead to the conclusion that the 
luminous sheath of ordinary gas flumes is at least one hundred and twenty 
degrees lower than the corresponding region in the acetylene /lame. 
Luminous flames of ordinary illuminating gas would perhaps repay 
further study, but owing to the fact that such gas is an ever varying 
mixture and that it is burned under conditions of pressure, etc.. such as 
to give a fluctuating character to the flame, the problem would have 



best an indefinite character from which studies of acetylene are free. In 
the latter case we have to deal with a definite fuel, and the velocity of 
the jets of gas from the burner is sufficient to give a high degree of sta- 
bility to the flame. 

The caudle would seem an even less satisfactory subject of study in 
these respects than illuminating gas, but the fact of the melting down 
of Wollaston wire, the verification of which I have briefly described in 
an earlier paragraph of this paper, seemed to discredit so completely the 
low values commonly given that I decided to redetermine its tempera- 
ture by the method already described. 

The fact that the flame of a candle, mounted upon a fixed stand, 
would move steadily downward as the material of which it was com- 
posed burned away, made it convenient, without any serious modifications 
of my apparatus, to explore the temperature of the luminous sheath 
throughout the entire length of the flame. It was only necessary for 
this purpose to mount a candle upon the steel bar in the position previ- 
ously occupied by the acetylene flame, and when it had reached such a 
length that the level of the rim of the cup lay below the level of the 
junction, to move the candle toward the latter by means of the microm- 
eter screw until the junction began to be submerged in the luminous 
sheath of the flame. It was then easy by a series of slight adjustments 
of the flame to explore with the junction the eutire surface of the lumi- 
nous sheath from base to tip, measuriug temperatures from time to 
time, and determining the position by means of the height of the junc- 
tion above the rim of the candle cup. The latter observations were 
readily made by means of the image of the candle upon the ground 
glass of the camera. Explorations of the candle flame in the manner 
described were made with Junctions II. and IV., and the results obtained 
showed a degree of consistency much greater than the fluctuating char- 
acter of the source under observation had led me to expect. Both sets 
of observations showed a maximum of temperature in the same region : 
that lying just above the tip of the interior dark zone of the flame. 
Readings were made by watching the movements of the candle flame 
and securing a balance of the potentiometer at times when the face of 
the junction was as nearly as possible in contact with, but not deeply 
submerged within, the luminous layer. Whenever the wire plunged to 
any considerable depth beyond the luminous surface, deposition of soot 
occurred with lowering temperature, and it was necessary to withdraw 
the junction into the non-luminous regions outside and to wait until the 
deposit had been burned off, before proceeding with the readings. In 


computing the actual temperatures of the luminous sheath of the flame 
from these readings, I contented myself with the following rough ap- 
proximation. The maximum temperatures shown by Junctions II. and 
IV. were plotted upon the same diagram used for the luminous »as 
flame. These temperatures were 1281° and 154G ; values which, as 
will be seen by inspection of -Figure 14 (c), lie much below those of the 
corresponding readings for the luminous gas flame, but in such position? 
as to make it easily possible to draw through them a curve analogous 
in form to that obtained for the latter. Such a curve would cut the 
line of zero cross-section at about 1670°, which may, I believe, be taken 
as the approximate temperature of the hottest portions of the luminous 
sheath of the candle flame. Estimates of this temperature by the prob- 
ably less accurate methods of drawing a straight line through the points 
in question and taking the point in which this line cut the line of zero 
cross-section to be the temperature of the flame, and estimates based 
upon the assumption that the true temperature is as many degrees above 
the temperature indicated by Junction IV. for the candle as it is for the 
gas flame, would lead to values respectively twenty-four degrees and 
forty degrees lower than that obtained by the method which I have 
adopted. I believe that the temperature just given (1670°) is much 
closer to the truth than that obtained under either of the other assump- 
tions. Estimated temperatures for other portions of the luminous sheath 
were made by assuming that the correction to be applied to the readings 
obtained with Junction IV. would be the same in all positions. TIi 
values are given in Figure 14 which may serve in place of an ordinary 
table. The portions of the flame to which each reading refers are 
more readily indicated by giving such a diagram of the flame than in 
any other way. 

The fact that, in the case of the acetylene flame and the ordinary gas 
flame, this method gives values high enough to account, for the melting 
of platinum, but leads to an estimate of the temperature of the candle 
flame which is about one hundred degrees below the melting-point of that 
metal, would seem, at first sight, to throw the procedure into serious 
doubt. My experience with the method has, however, been such as to 
make an error of one hundred degrees in the estimation of the candle- 
flame'temperature seem highly improbable. Messrs. Lurnmer and Pring- 
sheim, in a recent communication to the German Physical Society,* give 
an estimate of the temperature of candle flames based upon a relation 

* Lummer and Pringsheim, Verhandlungen der deutschen pliysikalischen 
Gesellschaft, 1899, p. 214. 



which they have established between the position of the maximum in the 
energy curve of the spectrum of a source of light and its temperature. 
Assuming the radiating substance in the flame to have the properties of 
a black body, they find this temperature in the case of the candle flame to 
be 1687°, a value seventeen degrees above that which I have given. 

To account for the fusion of Wollaston wire in the flame of a candle, 
one might consider the possibility of the existence in such a flame of 
layers of gas the temperature of which is much above the surrounding 
regions, and that these layers may be so thin that it would not be possi- 
ble to submerge the thermo-junction completely in them. In such a case 
the junction would give a value approximate to the average of the tem- 
peratures of the gases with which it was brought into contact. Before 
assuming this structure of the flame, which really has nothing to support 
it save the necessity of accounting for the apparent discrepancy which I 
have just pointed out, it seemed wise to consider, on the other hand, 
whether the melting-point of the Wollaston wire was necessarily that of 
pure platinum. Such wires would naturally be made of ordinary com- 
mercial metal, the melting-point of which might vary considerably from 
that of the purer platinum used in the determination of melting-points. 
It is likewise readily conceivable that in the process of drawing within 
the silver coating, a certain amount of silver might be worked into the 
pores of the platinum and not be removed by the subsequent action of 
the nitric acid. The determination of the melting-point of even such 

minute wires is fortunately a simple matter 
by means of the form of thermo-element 
used in the calibration experiments already 
described. It is only necessary to wrap a 
piece of the wire to be tested around the 
junction, as shown in Figure 15, to cut it off 
so that the end of the loop extends slightly 
(about 0.05 cm.) beyond the face of the 
junction ; and having mounted the juuction 
in the usual manner, to move the acetylene 
up to it by means of a micrometer screw. I 
performed this experiment with a piece of the same Wollaston wire 
which I had succeeded in melting in the candle flame, and found its 
melting-point, as indicated by the electro-motive force of the junction, to 
be 1674°. To test the question whether this very low melting-point 
was due to the presence of silver undissolved by the nitric acid, a piece 
of the same wire was left in the acid for twelve hours, after which the 

Figure 15. 




melting-point was again tested in the manner just described. The result 
of this determination was 1687°. The latter reading was, I think, too 
high, since subsequent examination under the microscope showed that 
the loop of the wire behind the junction had been melted so that the 
junction was probably a few degrees too hot. It may safely be conclude 1 
from these determinations that the melting-point of the Wollaston wire 
was at least one hundred degrees lower than that of pure platinum. 

Method of Checking the Constancy of the Acetylene Flame. 

To secure as complete a check as possible upon the constancy of the 
flame, the following method, based upon the assumption that so long as 
the radiation from the flame remained constant, its light-giving power 



Figure 16. 

would not vary, w r as employed. A diaphragm (d, Figure 16) similar to 
that interposed between the slit and the flame, and having an aperture of 
the same size, and mounted on the opposite side of the latter and a thermo- 
pile p, was placed at a distance of about 15 cm. from this opening. A 
second diaphragm, d' , with an intervening air space, served to cut off, in 
large part, the radiation from the heated metal. Two thin sheets of 
glass forming the sides of an empty cell c, of the kind used in the study 
of absorption spectra, etc., were placed between the cone of the thermo- 
pile and the second diaphragm ; so that only those rays from the (lame 
which were transmitted by the glass fell upon the face of the pile. 

The thermopile was connected with a sensitive d'Arsonval galvano- 
meter g, the circuit being kept permanently closed ; and a double metallic 
shutter s, which could be raised or lowered so as to open or close the 
opening in the diaphragm next to the flame, was so mounted that it could 
be readily operated by an observer at the telescope of the galvanometer. 
When a reading of the radiation from the flame was to be made, the 
zero point of the galvanometer was noted, and this shutter was raised 
during the short interval of time necessary to bring the needle, which 
was Dot strongly damped, to its first turning point. The shutter was 


then immediately closed in order to prevent further heatiug of the face 
of the thermopile. This throw of the galvanometer was taken as an 
indication of the intensity of the flame. 

It was found that the thermopile would cool sufficiently within two 
minutes to admit of the repetition of the reading. These observations 
were taken by an assistant simultaneously with each setting of the 
spectrophotometer, the intention being to reject any spectrophotometry 
readings made at a time when the flame showed marked deviation from 
its standard intensity, and to reduce the readings to a uniform flame 
intensity under the assumption that for the small range of variation 
occurring from reading to reading, the change in the brightness of the 
flame would be proportional to the variations of this galvanometer read- 
ing from the mean of the whole set. In point of fact it was found that 
the flame rarely varied from the mean in the course of a set of observa- 
tions by more than one per cent. From day to day, indeed, its intensity 
was usually within the limits stated above. Occasionally a larger varia- 
tion was detected. None of these variations in the course of the present 
investigation reached values so great as to lead me to hesitate to apply 
the correction already referred to, and all the observations described in 
this paper have been reduced to a constant flame intensity by means of a 
correction factor obtained from the readings of the galvanometer. 

Control and Measurement of the Temperature of the Carbon Rod. 

The carbon rod, having been brought to the desired degree of incan- 
descence by means of the current from a storage battery, was held at a 
constant temperature by varying the resistance placed in the battery 
circuit. The indications of the thermo-element inserted in the rod were 
noted by means of the potentiometer. The cells used in the measure- 
ment of the temperature of the carbon rod were the same as those em- 
ployed in the calibration pf the thermo-elements and in the study of the 
temperature of the acetylene flame. 

The potentiometer having been balanced by looping the circuit con- 
taining the thermo-element around a sufficient portion of the resistance 
box to balance its current against that of the Clark cells, a condition 
which was indicated by the reduction of the galvanometer deflection to 
zero, the current was maintained at such a value as to hold the carbon 
at a constant temperature during the time necessary to complete meas- 
urements of the intensity of eight different portions of the spectrum, 
ranging from the extreme red to violet, with the corresponding portions 
of the spectrum of the flame. In order to insure the maintenance of this 


constant temperature in the rod, an assistant made repeated observa- 
tions with the potentiometer and readjusted the resistance in the 
battery circuit whenever necessary. Excepting at very high tempera- 
tures, where the rod was subject to rapid disintegration, it was rarely 
necessary to make any adjustment during the progress of a single set 
of observations. Readings of the current flowing through the carbon 
and of the fall of potential between its ends were made at the beginning 
and end of each experiment. 

Spectrophotometry Observations. 

It was my expectation, in planning this research, that whatever might 
prove true as to the character of the radiation from gray carbon, Lhe 
distribution of energy in the spectrum from black carbon would change 
in such a manner with increasing incandescence as to become nearly or 
quite identical with that of the various luminous gas flames at tempera- 
tures corresponding to the temperature of the glowing carbon in those 
flames. I had also hoped, among other things, to be able to bring about 
a degree of incandescence approaching that of the acetylene flame itself, 
before the usefulness of the thermo-element as a means of measuring 
the temperature failed because of the melting of the platinum wire, and 
in this way to obtain a check upon my previous measurements of that 
flame ; and at the same time to be aide to determine the temperature of 
any given luminous flame in which the incandescent material consists 
of carbon particles by ascertaining the temperature of the carbon rod 
for which its surface had a spectrum corresponding in distribution of 
energy to that of the flame. 

It will be seen from inspection of the curves to be discussed in a 
subsequent paragraph that this expectation was far from being realized, 
and that the distribution of energy in the spectrum of the carbon rod. 
instead of approaching that of the acetylene flame as the temperature of 
the rod increased, took on an entirely unexpected character. Even at 
low temperatures, that is to say up to about 1100°, the change in the 
spectrum was not of the comparatively simple character which had been 
anticipated, and shortly after passing the temperature of 1100°, unlooked 
for complications in the results arose. The energy in the yellow of the 
spectrum which from the beginning had been increasing at a relatively 
more rapid rate than either in the red or at the blue end, became so 
great as to give the distribution curve a form entirely contrary to 

I was very slow to believe in the integrity of these results, and nearly 


a year was spent in repetitions of the measurements before I could con- 
vince myself that the phenomenon was a genuine one. Measurements 
taken upon a great number of different rods and at different times 
showed the same result, however, and I was finally forced to the con- 
clusion that the radiation from the carbon rods showed a much more 
complicated law of distribution than had been anticipated, and that a 
sort of selective radiation occurred such as to render the establishing 
of any simple relationship between the curve of distribution and tem- 
perature out of the questiou. 

The hope of being able to make direct temperature measurements up 
to the melting-point of platinum was also disappointed. While the 
carbon rods at comparatively low temperatures showed a fair degree of 
stability under the action of the current, they appeared to undergo a 
decided change of behavior at about 1400°, and before that temperature 
a rather rapid disintegration, showing itself by a change of resistance, 
manifested itself. This effect appeared to be similar to that which 
shortens the life of the filaments of incandescent lamps when these are 
subjected to a large amount of current. It appears, moreover, that at 
these high temperatures the carbon tends to combine with the metals 
of the thermo-element, affecting the electromotive force very much as 
the vapors in a furnace have been found to do. The thermo-elements 
inserted in the rod begin, in consequence of this action, to fail of their 
purpose. It was found that after exposure to temperatures much above 
1400°, the electromotive force corresponding to even lower temperatures 
was considerably below the normal. I svas consequently compelled to 
abandon the attempt to measure directly temperatures above this point, 
although it was possible to bring the rods to a higher degree of incan- 
descence for a length of time sufficient to perform the spectrophotometric 
observations. In order to obtain at least an approximate estimate of 
these temperatures, T made use of the fall of potential between the 
terminals of the rod, and also of the current of the heating circuit ; and 
by extending these curves, which, throughout the range of measured 
temperatures were found to be nearly straight, to the high temperatures 
which I wished to estimate, to obtain some idea, even if not an exact 
one, of the latter. 

In expressing the results of the photometric measurements already 
described, I have made use of two forms of curve. One set of curves, 
in accordance with the nomenclature proposed in my original paper on 
the visible radiation from platinum, and later adopted by Paschen and 
other writers, I may call isotherms. These curves give in terms of the 




<f- t**vtrea* 

5oL ca*-£ 





frt£*n*r- / 1 


C^H^ ao rf- 
















/ /7^° 




' / 











' / 




- — ^ 


r « ?J0° 




— — • 


_ — — — » J 



^. poo' 


Figure 17. 


corresponding wave lengths of the comparison source (in this case the 
acetylene flame), the relative distribution of energy in the visible 
sprctrum from the carbon rods. The other curves, which I have termed 
tsochroms, indicate the rise in the energy of any particular wave length of 
the visible spectrum, with increase of temperature. Each of these curves, 
taken by itself, is entirely independent of the nature of the light of the 
comparison source, but the absolute relation of such curves to one another 
can only be obtained when we know the distribution of energy in the 
spectrum of that source. By means of the isochroms, it is, however, 
possible even without this knowledge to compare the rise in intensity 
of any single wave length of the spectrum with increasing temperature. 
The set of curves shown in Figure 17 are plotted directly from obser- 



vations upon a black (untreated) carbon at temperatures ranging between 
795° C and 1055° C. In tbis diagram abscissae are wave lengths and 


Zoo" /r //oo" 




\7 a f* 


! i 


~/ T 

/ / 

K / 

/ / 
/ / 

1 L. 

/ / 

/ / 

I I 
I I 
I I 

i I 

— 7 — T 











foo e /ooo° 

Figure 18. 


ordinates are ratios of the brigbtness of the spectrum of tbe carbon rod 
in each region to that of the corresponding region in the spectrum of 



the acetylene flame. A noteworthy fact exhibited by means of these 
curves is the relatively rapid increase of intensity in the middle of the 
spectrum. In passing from 930° to 1055° the brightness of wave 
length .7C p, increases 5.3 times ; that of .70 p, 7.2 times ; that of .60 p, 
13.5 times, and that of .50 p o>dy 9 times. We have here the beginnings 
of a process which becomes more marked in its effects as higher temper- 




c ce*>. 





aM. , 








! , 

' / 




/ i 


1 1 


1 1 



1 1 



i ' 



/ ' 



/ / 




/ i 








/ / 








* i 

» f 















/ i 





























IOOO" nOQ a /lOO° /ZOO' 

Figure 19. 

atures are attained. From 1100° upwards it was found much more 
difficult to obtain satisfactory readings. The carbon rods which I had 
brought from Paris for this investigation would not stand prolonged 
heating and it was necessary to replace them frequently. 


In order to bring the observations upon the various rods to a common 
scale, isochroms from the readings for each rod were plotted. The gen- 
eral character of these curves is shown in Figure 18, in which the isochroms 
corresponding to the isotherms of Figure 17 are given. From the ordinate 
at 1000° of the isochrom for .G/.i, which for convenience was taken as 
unity for the entire set, a reduction factor was obtained by means of which 
all the curves for all the carbons were brought to the same scale. A new 
set of isochroms was then plotted for each of the wave lengths .75^, .70^, 
.65^, .60^, .55//, .50(i, and .45^, in the drawing of which all the obser- 
vations upon the rods were used. While this method did not bring the 
various sets of observations into perfect agreement, the results were 
sufficiently definite to indicate with a close degree of approximation the 
trend of these curves for temperatures up to 1400°. The result of this 
compilation for the wave lengths just mentioned is shown graphically in 
Figure 19. From these curves in turn, isotherms for the temperatures 
900°, 1000°, 1100°, 1200°, 1300°, and 1400° were plotted. These curves 
are given in Figure 20. Had the law of increasing intensities throughout 
the spectrum with rising temperature been that anticipated at the begin- 
ning of this investigation, the trend of the isochroms would necessarily 
have been such as to bring all the curves together at a common point 
corresponding to the temperature of the acetylene flame. In other words, 
if the spectrum of the acetylene flame were identical throughout with that 
of the carbon rod at the same temperature, the isotherm of the spectrum 
of the rod at that temperature would be a horizontal line. It is obvious, 
however, that if the wave lengths of the middle of the spectrum should 
continue to increase faster than the red and the violet, a condition would 
presently be attained in which the ordinate of the isotherm would be 
greater in the yellow or green than at either end of the spectrum. We 
see indications of the approach of this condition in the diagram of iso- 
chroms (Figure 19), from which it is evident that the curves for .65/i and 
.60/i would cut each other and would cut the curve for ,70ft at some tem- 
perature not far above 1400° ? whereas the isochroms for the shorter 
wave lengths would not be likely to cut the curves for the red until some 
much higher temperature had been reached. 

The curves in Figure 20 show the nature of this unexpected development 
of the spectrum in a somewhat different aspect. It will be seen from 
this figure that the growth in the extreme red so far lags behind that of the 
full red, and this in turn behind that of the orange, and this in turn 
behind that of the wave length .6^, that at 1400° the isotherm, instead of 
being convex to the base line throughout, actually becomes convex. 1 



have indicated by means of lighter lines the form of curve which might 
have been expected had the type of isotherm which exists at lower tem- 
peratures been maintained. 

Ahove 1400° it was found impossible to obtain consistent readings on 
account of the rapid disintegration of the carbon rods ; but I was ahle to 
satisfy myself after repeated trials that at temperatures not far above 
1500° this change in the character of the isotherms had progressed to the 

y^O fac^~<! firr 



* cU'. </*&-) 

f+m.fa&a2LcC £&A.lri 









! S 






: / 








9oo m 


FlGURE 20. 


point at which the yellow regions of the spectrum possess an ordinate 
greater than that of the extreme red or of the blue or violet. At a tem- 
perature about 300° below that of the acetylene flame, then, the spectrum 
of the carbon rod was relatively weaker in the red, stronger in the yellow, 
and weaker again in the shorter wave lengths than the spectrum of the 
Maine. There is no reason to suppose that had it been possible to heat 
the rods to the temperature of the flame itself the law of increase of 
intensity for the various wave lengths would have undergone such radical 
modifications to bring the two spectra at that temperature into identity. 



Spectrophotometric Measurements upon Rods with Treated Surfaces. 

In order to compare the radiation of rods of black surface with those 
the surfaces of which have acquired a gray coating by treatment in 
hydrocarbon vapor, rods were mounted in the usual manner, and after 
the exhaustion of the air from the metal box, gasoline vapor was allowed 
to enter until the atmosphere surrounding the rod was saturated. The 

Figure 21. 

rod was then brought several times to a high state of incandescence for 
a few seconds at a time, by which means the entire surface became coated 
with a gray deposit of carbon similar to that obtained by the treatment 
of incandescent lamp filaments. The metal box was then again pumped 
out and spectrophotometric measurements similar to those already de- 
scribed were made upon the radiation from the treated surface. It was 
thought that as the result of this treatment the carbon rods would stand 


a more prolonged exposure at high temperatures, and that thus it might 
be possible to extend the measurements beyond the point reached with 
the rods of black surface. This was found to be the case. 

As has already been indicated in a previous paragraph, the indications 
of a thermo-junction at these high temperatures was subject to serious 
suspicion. I was obliged to content myself, therefore, with estimations ol 







/ / 



1 / 

1 J 







: i 

































• -""■ ~ " 

= -::: 





.6 ii. 

Figure 22. 

./ ix 

the temperature based upon the difference of potential between the ter- 
minals of the rod. Fortunately the relation between the electromotive 
force and the temperature up to 1400° was of such a character that but 
little error was to be feared in extrapolating. The relation between 
electromotive force in volts and temperature is shown in Figure 21. 
From this curve temperatures above 1400° were determined. 


The work upon treated carbons was confined chiefly to high tempera- 
tures, a sufficient number of readings within the range already explored 
with the untreated carbons being taken to show that the distribution of 
intensities at the lower temperatures did not differ materially from that 
in the spectrum of the former. The set of isotherms given in Figure 22 
will suffice to indicate the general character of the results. It will be 
seen that in this case, as in that of the untreated carbon, the concavity of 
the curve between .6^ and the red end of the spectrum is well marked 
at 1365° ; and that at 1515° there was a well-pronounced maximum at 
about .65^. The greater stability of the treated carbon made it possible 
to obtain consistent measurements on a number of rods at temperatures 
above 1500° and to establish beyond doubt the form of the curves. It 
is obvious that for the study of the spectrum of incandescent carbon at 
this and higher temperatures the conditions would be much more 
favorable in the case of the incandescent lamp than with rods mounted 
in a large vacuum chamber like that used in the present investigation. 
Lamp filaments in the process of manufacture are brought by thorough 
carbonization into a condition to withstand permanently much higher 
temperatures than the rods at my disposal were capable of doing. 
There is as yet, it is true, no direct means of determining the tempera- 
ture of the lamp filament ; but the curve for the relation of electromotive 
force to temperature (Figure 11) is of such a character as to lead us to 
expect that comparisons of the spectra of incandescent lamps, in which 
electromotive forces were used as a criterion of the decree of incan- 
descence, would at least enable us to confirm the existence of the 
remarkable phenomenon brought out by the present experiments and to 
extend observations of it to still higher temperatures. 

Mr. Ernest Blaker has, since the completion of the measurements 
described in this paper, compared the visible spectrum of lamps with 
treated filaments, and of lamps the filaments of which before exhaustion 
had been coated with lampblack, with the spectrum of the acetylene 
flame. His measurements confirm very completely those which I have 
described in this paper, and contribute important evidence in favor of the 
existence of this anomaly in the law of distribution of intensities in the 
spectrum of glowing carbon. 

Theoretical Aspects of the Foregoing Data. 

The efforts of students of radiation have of late years been directed 
particularly to the testing of the various formulae by means of which 
the mathematical physicists have attempted to express the intensity of 


radiation as a function of wave length and temperature. The equation 
reached from quite different points of view by Wien * and by Planck, f 

/= Cl A -5 e-Ar' 

in particular, has been the subject of exhaustive discussion and of 
experimental tests. To this end Paschen $ determined with the bolo- 
meter the distribution of energy in the infra-red spectra of various 
bodies from 15° C to 1300°. The materials thus subjected to measure- 
ment were oxide of copper, platinum, lampblack, and graphitic carbon. 
The range of wave lengths explored extended from 9.2/t to 0.7 ( «. 
Luiumer and Pringsheim § made similar determinations upon the ideal 
black hotly, and Lummer and Jahnke || finally repeated these measure- 
ments in the case of the black body and of platinum. Wanner,! working 
with Paschen, made careful spectrophotometric measurements of the 
visible radiation from the ideal black body. To test the applicability of 
the Wien-Planck formula to these measurements, the equation is given 
the form, — 

log 7= -vi — y» y> 

in which 

yi = log (<?! A -5 ), 

72 = ^ log e. 

The isochromatic curves are then plotted with the logarithm of the 
intensities as ordinates and the reciprocal of the absolute temperature as 
abscissae. The agreement of the equation with the observations is 
found in the fact that isochroms thus plotted, at least as far as the work 
of Paschen and Wanner is concerned, always take the form of straight 
lines, and that the quantity r 2 computed for various wave lengths is 
found to be a constant. Lummer and Pringsheim, on the contrary, find 
in the discussion of their measurements that the constant, c 2 increases 
steadily with the wave length from 13,500 at 1.2 p to 16,500 at 5 p, and 
18,500 at 0.3 p. The value of c 2 computed by measurements from 

* Wien, Wiedemann's Annalen, LVIII. 662 (1896). 

t Planck, Drude's Annalen, I. 69 (1900). 

t Paschen, Wiedemann's Annalen, LVIII. 455 (1896); also LX. 662 (1897). 

§ Lummer and Pring-sheim, Deutsche phys. Gesellsehaft, I. 23, II. 16o (1900). 

|| Lummer and Jahnke, Drude's Annalen, III. 283 (1900). 

1 Wanner, Drude's Annalen, II. 141 (1900). 



Beckman at wave length 24 was found to be 24,250. Lumraer and 

Pringsheim find, moreover, that the logarithmic isochroms, especially 

when extended to higher temperatures, are not straight lines, but show a 

, . 1 
slight convexity towards the — axis. 

Exception has also been taken to the Wien-Planck formula on the 
ground that it gives for infinite temperatures a finite limit to the value of 
the intensity, a result which Rayleigh * in a recent paper has character- 
ized as physically improbable. 

Rayleigh proposes the form 

. — 4 — 



I= Cl T\~ % e~^T 

but Lummer and Pringsheim find that this likewise fails to properly express 
their experimental results. Lummer and Jahnke propose, in view of 
these discrepancies, to give the equation the general form 

/= CT 5 (XT)-* e-(^) v ' 

an expression which coincides with Wien's formula for ft = 5 and with 
Rayleigh's for [i = 4. They find the measurements of Lummer and 
Pringsheim satisfied when p lies between 4.5 and 5, and v lies between 
.9 and 1.0. If we accept the value /< = 5 and v — 0.9, this equation 
always leads to a finite value of intensity for infinite temperature. All 
other values of these quantities give infinity as the limit of intensity. 

Whether logarithmic isochroms or the value of the quantity c 2 , computed 
from measurements upon carbon rods, would aid in deciding between the 
various equations under discussion is a question. The data given in this 
paper would not lead us to class the carbon rods studied as black bodies. 
The emissive power of various forms of carbon is well-known to be 
smaller than that of the ideal black body, and there is no reason to 
suppose that it is independent of the temperature. The relative lagging 
behind of the intensities in the red might perhaps be taken a3 an indica- 
tion of a tendency to approach the infinite maximum demanded by the 
Wien-Planck formula ; but the isochrom for .76 shows that the effect, if 
it exists, must be looked for at some much higher temperature than that 
covered by these measurements. In spite of these doubts as to the 
applicability of the measurements on carbon rods to the problem of the 

* Philosophical Mag., XLIX. 539 (1900). 




law of radiation of the ideal black body, I have plotted the various iso- 
chroms obtained in the course of this investigation in logarithmic form ; 
absolute temperatures being taken as abscissae and the logarithm of the 
intensity as ordinates. These logarithmic isochroms, as will be seen from 





Figure 23. 

Figure 23, in which three curves from Figure 19 are reproduced, are 
straight lines. The range of temperatures is doubtless much too small 
to bring out the curvature found by Lummer and Pringsheim, but the 
curves show clearly the change of direction with the wave length men- 



tioned by those writers on page 222 of their paper before the German 
Physical Society.* 

For very high temperatures no experimental data for the radiation 
from carbon exist excepting the measurements described by Lucas, f It 
has been rather the fashion to leave Lucas's work altogether out of 
account as being hopelessly at variance with more recent results. Kay- 
ser, $ for example, after giving Lucas's data, says, — 





/ / 
/ / 

/ / 

/ * 


200 i 














1- J»' 


Jcroo" 2ooo° 3ooo' 

Figure 24. 


Zu jahchen Schliissen gelangt audi Lucas, durch Versucke welche das 
Verdampfen der Kohle in Frage zu stellen scheinen. 

His results, nevertheless, which I have given graphically in Figure 24, 
appear to me to be of significance. His formula for the relation of tem- 
perature to current, t = 25 i, must of course be regarded as only ap- 
proximately correct even at moderate temperatures. The curve for the 
relation between the current in a carbon and the temperature, up to about 

* Lummer and Pringsheim, Verhandl. d. Deutschen Physikal. Gesellscli (1899) 
p. 222. 

t Lucas, Comptes Rendus, 0. 1454 (1884). 
% Kayser, Handbuch der Spectroscopic, I. 157. 


1500°, does however not vary widely from a straight line. Beyond these 
temperatures it is a matter of extrapolation, but the same thing is true 
of all other attempts to estimate very high temperatures. The curve /, 
for the relation of the logarithm of the intensities and the temperatures, 
which I have also given in Figure 24 (between 1500° and 3750°), is in 
the case of Lucas's measurements nearly straight ; so that in so far as 
this is a criterion, his curve up to this point may be said to conform to 
the Wien -Planck equation. It is significant that Lucas's curve shows an 
inflection point between 3.300° and 4000°, becoming concave to the 
axis of temperatures. This is the temperature at which, according to 
nearly all the newer determinations, carbon, as in the crater of the arc, 
approaches its maximum condition of incandescence. At about 3750° 
the electrical energy developed in the rod is doubtless largely expended 
in the disintegration or vaporization of the carbon, so that a maximum 
degree of incandescence is approached. At the point at which this process 
begins current can no longer betaken as a measure of the temperature. 
The very slight falling off in the photometric measurement of intensity 
does not appear to me to warrant the conclusion drawn by the author that 
a maximum has been passed at the current value to which he assigns 
the temperature 4750°. The difficulty of obtaining consistent readings 
under conditions existing in such work would amply account for so slight 
a discrepancy. 

Lucas's work appears, in a word, to warrant the following rather 
important conclusions. First, that up to about 3750° current and 
temperature in the case of carbon rods heated electrically are nearly 
proportional. We have in favor of this point two checks, — the straight- 
ness of the logarithmic curve and the fact that the inflection of Lucas's 
curve corresponds, as has already been pointed out, to the recognized tem- 
perature of the crater of the arc. Secondly, that for a wide range of 
temperatures photometric intensity, like the intensity of total radiation, 
follows the logarithmic law of iucrease. Third, that after the tempera- 
ture of the crater has been attained a considerable additional increase in 
incandescence results from the application of further current before the 
maximum is finally attained. This agrees with the observations of 
Moissan,* that many reductions in the electric furnace which do not 
occur with moderate currents become possible by increase of the current 
strength. If, as seems proper, we ascribe the rapid approach of Lucas's 
curve to a finite maximum to the utilization of the energy of the cur- 

* Moissan, Comptes Kendus, CIX. 776 (1894). 


rent in disintegration of the carbon, it follows that no definite tempera- 
tures can be given above the point of inflection. Lucas's measurements, 
therefore, cannot be said to throw any light upon the question whether 
the intensity of radiation of incandescent bodies reaches a finite limit as 
demanded by the Wien-Planck formula. The lower portion of the 
curve shows no approach to such a maximum. Whether the study of 
radiation, wave length by wave length, up to the temperature of the 
crater will be found to do so remains to be seen. Far beyond that tem- 
perature experiments with carbon can probably never be carried ; so 
that the final determination of this point must probably be reached by 
experiments on some more refractory material. 

In the prosecution of portions of this investigation I have received 
valuable aid from Drs. C. H. Sharp and Leopold Kann and from Mr. 
L. W. Hartman, to all of whom I desire to express my obligations and 
extend my hearty thanks. 

Phtsical Laboratory of Cornell University, 
April 24, 1901. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 5. — September, 1901. 


By Halcott C. Moreno. 

By Halcott C. Moreno. 

Presented by W. E. Story, May 8, 1901. Received June 1, 1901. 

The present paper is a discussion of those loci in n-fold space that 
can be generated by flats whose equations involve a single arbitrary 
parameter. The ruled loci of space of three dimensions can be repre- 
sented in this way. 

I. Loci derived from an (n — 1)-flat whose Equation involves 
a Single Arbitrary Parameter; Developables. 

1. Description of the derived loci. 

Let us consider the loci derived from the equation 

A = 0, 

the equation of an (n — l)-flat involving a single arbitrary parameter A. 
If the parameter enters rationally, we suppose it to enter to as high a 
degree as n, the number of ways of the space. If the parameter enters 
rationally to the degree m where m < ?i, the locus is of a special kind to 
be discussed later. As the parameter varies continuously we have a 
1-fold infinite system of (11 — l)-flats. 

Two consecutive (« — l)-flats of the system intersect in an (n — 2)-flat 
whose equations are 

If from these equations we eliminate the parameter there remains a 
single equation of an (n — l)-spread, S n _^ which is ruled by the 1-fold 
infinite system of (n — 2)-flats. 

Three consecutive (n — l)-flats of the system intersect in an (n — 3)- 
flat whose equations are 

a a ^ A 9-A 


These (ft — 3)-flats may be considered as arising from the intersection 
of two consecutive (ft — 2)-flats of the system of (ft — 2) -flats. The 
elimination of the parameter from these equations gives a restricted sys- 
tem equivalent to two independent equations. The system represents an 
(n — 2)-spread, S n _ 2 , which is ruled by the (ft — 3)-flats. 

In like manner r consecutive (ft — l)-flats of the system intersect in 
an (n — r)-flat whose equations are 

A 9 A n 9 r ~ 2 A 

A = , _ = „,... ^ = o. 

Any of these (n — r)-flats may be considered as arising from the inter- 
section of two consecutive (ft — r + l)-flats of the system of (n — r + 1)- 
flats that are the intersections of r — 1 consecutive (ft — l)-flats of the 
system. The elimination of the parameter from these equations gives 
a restricted system equivalent to r — 1 independent equations. These 
equations represent an (n — r -f l)-spread, S n _ r + l , which is ruled by the 
1-fold infinite system of (ft — r)-flats. 

The locus of the intersections of n consecutive (ft — l)-flats of the 
system is a curve, while n + 1 consecutive (ft — 1) -flats do not in 
general have any common intersection. 

We will use S k to denote that one of the related spreads of this system 
that is of k ways. It is geometrically evident that each one of these 
spreads is a developable spread.* 

Considered in this light we see that the (ft — 2)-spread is a double 
spread on S n _i corresponding to the cuspidal edge or edge of regression 
in ordinary threefold space."} - 

The S n _ s is a double spread on S n _ 2 , etc., and S : on S»> We see also 
that $„_g is a triple spread on *S', i _ 1 ; Killing calls it doubly stationary. 
Finally, S t is an (ft — l)-tuple curve on £„_! ; it is a multiple curve on 
all the other spreads of the system. J 

If the equation 

A = 

contains k arbitrary parameters connected by k — 1 equations 

<£ = 0, x = 0, ^ = o, 

* Killing, Nicht-Euklidische Raumformen, p. 195 et seq. 

t Puchta calls the S„—i the most general developable spread in w-fold space. 
Puchta, Ueber die allgemeinsten abwickelbaren Riiume, ein Beitrag zur mehrdi- 
mensionalen Geometric Wien. Berichte, CI. 

% Killing, loc. cit. 



we can, theoretically, solve these equations for k — 1 of the parameters 
in terms of the remaining one, so that this case is the same as the previ- 
ous one. 

The actual elimination may be avoided. Let the parameters be A, 
fjL, .... v. Differentiate totally all the equations, 

9 A 

9A ^ J A r1 
-7TT- « A + -pr- dfl + 

a A <y fx 


9 <f> 

9 <f> 

9 v 

dv = 

d\ + ^dfJL + + -^ dv = 

From these we may eliminate the differentials, 

9 A 9 A 9 A 

B = 

9 A 9 (i 

9 <f> 9 <f> 

9 A 9 (i 

9 v 

9 I 
9 v 

9 i[/ 9 ^ 

c/A 9 [i 

9 $ 
9 v 


This is the equation of an (n — l)-flat. The equation involves k 
parameters but they are connected by k — 1 equations. Two consecutive 
(n — l)-flats of the system intersect in an (n — 2)-flat whose equations 
are A = 0, B = 0. 

Three consecutive (re — l)-flats of the system intersect in the (re — 3)- 


A = 0, B = 0, C=0, 

where is the determinant B, with A replaced by B. The equation of 
the £„_! is found by eliminating the parameters between the equations 
of the (n — 2)-flats and the equations connecting the parameters. The 
equations of the other spreads are derived in a similar manner. The 
system of related spreads is of the same character as before. 

2. Mutual relations of connected loci. 

Let us consider more in detail these connected loci. We will use F k 
to denote a &-flat of the 1-fold infinite system of £-flats. Two consecu- 


rive i'Vi's intersect in an F n _ s , three in an F n _ 3 , r in an F n _ r , n — 2 
in an F. 2 or plane, n — 1 in an F 1 or line, n in an F or point. There 
is a 1-fold infinite system of these i^,_ 2 's which are generators of £„_!, 
a 1-fold infinite system of F n _ 3 s, generators of S n _ 2 , a 1-fold infinite 
system of lines generators of S 2 , the developable surface. 

Through any F n _ 2 there pass two consecutive F^s, through any F„_ 3 
there pass three consecutive -F„_i's, through any F , n consecutive F^s. 
Tlirough any F n _ z there pass two consecutive F„_ 2 's, through any F„_ 4 
there pass two consecutive -F n _ 3 's and three consecutive F„_2S,&nd so on. 

"We may then reverse this process and start with the curve of the 
system. Through any two consecutive points of the curve there passes 
a line, an F u through any three consecutive points an osculating plane, 
an F 2 , through any four consecutive points an osculating 3-flat, an F 3 , 
through any n — consecutive points an osculating (n — l)-flat, an F n _ v * 

That these operations may give unique results this curve must lie in 
the n-fold space and in no flat space of a less number of ways. If the 
curve lie in a £-flat, where k < n — 1, all the £-flats through h + 1 con- 
secutive points coincide and definite (k -f l)-flats are not determined at 
all. By a theorem of Clifford, such a curve must be of an order as 
great as ra.f 

This theorem has been generalized by Veronese.^ 

Let us consider any curve in n-foh\ space whose equations are, 

= 0, x = 0, . . . . if, = 3 

a restricted system equivalent to n — 1 independent equations. The 
equations of the tangent at any point P' of this curve are linear equa- 
tions whose coefficients are functions of the n non-homogeneous co- 
ordinates, x', y', . . . . v'. The same thing is true of the equations of 
any of the osculating flats at the point P. The osculating (n — l)-flat 
is given by a single equation, the coefficients of which are functions of 
these n quantities x', y', . . . v'. If we regard these as n parameters 
they are connected by the equations, 

^ = 0, x ' = 0, . . . . ip' = o,§ 

* We shall say a /t-flat osculates a curve if it contains k + 1 consecutive 
points of it. Killing, loc. cit. 

t Clifford, Classification of Loci; Mathematical Papers, pp. 305-331. 

i Veronese, Behandlung der projectivischen Verhaltnisse der Baume von ver- 
schiedenen Dimensionen durch das Princip des Projicirens und Schneidens, 
Mathematische Annalen XIX. 

§ <p' = <p (x>, y', . . . v>), etc. 


a restricted system equivalent to n — 1 independent equations. "We 
have then the case of an (n — l)-flat whose equation involves n para- 
meters connected by n — 1 independent relations ; this is equivalent to 
the case of a single equation containing one arbitrary parameter. We 
may, in general, consider the system of developables as given by an 
(» — l)-flat whose equation contains a single arbitrary parameter or 
k parameters connected by k — 1 equations.* 

3. The tangent (n — \)-flats that are common to n — 1 (n — V)-spreads 
envelop a developable. 

The equation in homogeneous coordinates of any (n — l)-fiat may be 


x = ay-\-j3z-\-.... J ! -yw. 

This equation involves n independent parameters; if we connect them 
by any n — 1 independent equations we shall have the equation of an 
(n — l)-flat that contains but a single independent parameter, so that 
the 1-fold infinite system of (n — 1) -flats represented by it envelop a 
developable. The tangent (n — l)-flat at any non-singular point of a 
developable S,^ contains the generating F n _ 2 through that point and 
touches the *S'„_ 1 all over this flat, t We may speak of this developable 
S n _! as enveloped by its tangent i^-i's. If then we impose on an 
arbitrary (n — l)-flat any conditions that give rise to n — 1 independent 
equations between the coefficients in its equation, the (n — l)-flat will 
envelop a developable S n _i. 

Let IT= 

be the equation of an (n — 1) -spread. The equation of the tangent 
(n — l)-flat at any ordinary point P' is 

9U< 3U> 9U> A 

If we impose on the equation of the arbitrary (n — l)-flat the condi- 
tions that it shall be this tangent (n — l)-flat, the coefficients in the two 
equations must be proportional. We must have then 

9U[ 9U[ 9U< 

9 x' = 9 y' = . . . . 9 w' 

— la y 

From these equations by means of the equation 

W = Q, 

* Salmon, Geometry of Three Dimensions, p. 286. t Killing, loc. cit. 


we may eliminate the coordinates of P' leaving a single equation in 
a, (5, .... y. For an (n — l)-flat to be tangent to an (?i — l)-spread, 
one relation between the coefficients that enter into their equations must 
be satisfied. We conclude then that the (n — l)-flats that touch n — 1 
(n — l)-spreads envelop an S n _ 1 . 

Let us consider only those tangent (n — l)-flats to an (n — 1)- 
spread that touch it at the point of an (n — 2) -spread that lies on it. 

Let £7=0 

be the equation of the (n — l)-spread and let 

U=0, V=0, ..., 

a restricted system equivalent to two independent equations, be the equa- 
tions of the (n — 2) -spread on it. We derive now the equations 

9U' 9 IP 9U' 

9x' =. 9 y' = . . . . 9 to' 

— la y 

and IP = 0, V = 0, ... 

If we eliminate the parameters from these equations there remains 
a restricted system equivalent to two independent equations in the 
coefficients a, (3, ... y. For an (n — l)-flat to be tangent to an 
(n — l)-spread at a point of an (n — 2)-spread on it requires two con- 
ditions between the coefficients in the equation of the (n — l)-flat. 
These two conditions may be used as part of the n — 1 conditions that 
connect the coefficients of an (n — l)-flat that envelops a developable 
S„-v We have then the theorem that the (n — l)-flats that are tangent 
to p (n — l)-spreads at the points of p (n — 2)-spreads that lie one on 
each (n — l)-spread, and are tangent to cr other (n — l)-flats, where 
n — 1 = 2 p -\- cr, envelop a developable. 

In a similar manner for an (n — l)-flat to be tangent to an (n — 1)- 
spread at a point of an (n — 3) -spread that lies on it imposes three con- 
ditions on the coefficients that enter into the equation of the (w — l)-flat. 
To be tangent to the (n — l)-flat at a point of an (n — 4) -flat on it 
requires four conditions, etc. To be tangent to an (n — l)-spread at a 
point of a curve that lies on it requires n — 1 conditions between the 
coefficients, which is just sufficient to make the {n — l)-flat envelop a 

We have then the general theorem that the (n — l)-flats that are 
tangent to p (n — l)-spreads at points of p (n — &) -spreads that lie one 


on each, tangent to o- (n — l)-spreads at points of cr (n — k -f l)-spreads 
that lie one on each, tangent to t (n — l)-spreads at points of t (n — 2)- 
spreads that lie one on each, and finally tangent to v other (n — 1)- 
spreads, where p, cr, . . . t, v, are non-negative integers connected by 
the relation 

n — 1 = k. p + (k — 1) o- + •••• + 2 t + v, 

envelop a developable S n _ v 

Similar cases occur in three-fold space where we have the tangent 
planes that are common to two surfaces enveloping a developable surface 
as do the tangent planes to a surface at the points of a curve on that 

4. Some additional properties of devehpables ; sections. 

Other properties of an S n _ x may be deduced by regarding it as the 
envelope of an (n — l)-flat whose equation involves a single parameter.! 
Through any point in space can be drawn a definite number of tangent 
i^n-j's to the S n _ v For substitute the coordinates of the point in the 
equation of the variable (n — l)-flat and there is a certain finite number 
of values of the parameter that satisfy the equation. 

Any F n _ x of the system meets its consecutive F„-\ in a definite F n _ 2 , a 
generator of S n _ t whose equations are, 

„ = o,fi = <, 

Any three consecutive i^-^s meet in a definite F n _ z , a generator of *^„_ 2 , 

whose equations are, 

. 9 A PA . 

A==0 >9X=°>W =0 - 

Any n — 1 consecutive 2 ?T B _ 1 's meet in a definite line F x , a generator of 
$2, whose equations are, 

. n 9A 9->A 

^ = 0,_=:0,. ..^=0- 

Finally, any n consecutive i^_ 1 's meet in a definite point of the curve of 
regression of S 2 . The equations of the F are, 

. . 9A 9^A 

* Salmon, Geometry of Three Dimensions, p. 547. 

t Salmon, Geometry of Three Dimensions, p. 289 et seq. 


In general n + 1 consecutive F n _^s do not have any common inter- 
section, for the n + 1 equations, 

have no common solutions. If we regard these equations as homo- 
geneous in the n -f 1 coordinates we may form their resultant, and the 
values of the parameter that cause this determinant to vanish, give 
special points where n + 1 consecutive F^s intersect. These points 
are cusps on the curve Si. 

Reciprocally there will, in general, be a finite number of F n _^a that go 
through n + 1 consecutive points of S^ 

Veronese has shown that a curve in n-fold space has 3 n singularities 
which are connected by 3 (n — 1) relations, an extension of the Pluecker- 
Cayleyan characteristics of a twisted curve in three-fold space.* 

In this we have assumed that the variables that enter into the equation 
of the enveloping (n — l)-flat cannot be expressed in terms of fewer 
than n + 1 independent linear functions of the variables alone. If they 
could be expressed in terms of v such linear functions, where v < n, the 
developable »S n _ 1 is a conoid with an (n — v)-way head, a case to be con- 
sidered later. 

The developable S k oi the series is ruled by (k — l)-flats, F k _ r 'a. The 
S u , where 2 < k ^ n — 1 can be given by means of its enveloping F k 
whose equations involve a single parameter. The n — k equations of the 
F k must however be of the form 

, n 9A n d n ~ k ~ x A n 

as we have previously seen. Even the S x may be represented in this 

Any (n — l)-flat B = 

cuts the £„_, in a developable (n — 2)-spread, for it cuts the system of 
F n _i& in a system of (n — 2)-flats that intersect consecutively in (n — 3)- 
flats. We may see this in another way. By means of this new equa- 
tion we can eliminate one variable from the equation of the enveloping 
(n — l)-flat. The resulting equation in n variables may evidently be 
considered as the envelope of an (?i — 2)-spread in a new (n — l)-fold 
space. The (n — l)-flat cuts any S k of the system in a (i — l)-way 

* Veronese, Ioc. cit. ; Killing, loc. cit. p. 197 et seq. 


developable. In general any r-flat where r > n — k + 1 cuts any S k in 
a developable (k + r — w)-spread. 

Any F n _ x of the system cuts the S n _ x in an (ft — 2) -spread, and the 
F n _ 2 that it has in common with the consecutive F n _ l appears twice in the 
intersection, so that the proper (ft — 2)-spread is of order less by two 
than the order of S n _ v This (ft — 2)-spread is also a developable. 

An F n _o is met by the consecutive F n _ 2 in an F n _^ ; it is met by any 
other F n _ 2 in an (n — 4)-flat. In general, where 4 < n, there are a 
2-fold infinite system of these (ft — 4)-flats and their locus is an (n — 2)- 
spread which is a double spread on S n _ v In the case of cones and 
conoids this double spread may be of fewer than n — 2 ways. Thus in 
four-fold space the planes which join a line to the successive points of an 
irreducible conic form a three-way developable. This developable is a 
conoid and the one-way head is the only multiple locus on the conoid. 
In three-fold space cones are the only developable surfaces that do not 
possess a proper double curve, if we call the cuspidal curve a double 
curve. In general there is a double curve distinct from the cuspidal 
curve. We will assume that we have the general case of a developable 
and not a cone or conoid. The total double spread on S,^ consists in 
general of two parts, S n _ 2 and 2„_ 2 , where 2„_ 2 is the locus of the 
2-fold infinite system of (ft — 4)-flats arising from the intersection of 
non-consecutive F^s, while S n _ 2 is the locus of the 1-fold infinite 
system of (ft — 3)-flats arising from the intersection of consecutive F„_ 2 s. 

Any three non-consecutive F n _ 2 s intersect in an (n — 6)-flat ; there 
are in general a 3-fold infinite system of such (n — 6) -flats whose locus 
is an (n — 3)-spread, a triple spread on S n _ 2 . Any (ft — G)-flat is the 
intersection of three (ft — 4)-flats of 2„_ 2 and any such (n — 4)-flat con- 
tains a 1-fold infinite system of such (ft — 6)-flats. This 1-fold infinite 
system of (ft — 6)-flats does not, in general, fill out the (ft — 4)-flat, for 
this would require a 1-fold infinite system of them. The total triple 
spread on S,,^ consists in general of two parts *S, ( _ 3 and 2„_ 3 where 2„_o 
is the locus of the 3-fold infinite system of (ft — 6)-flats. We can supply, 
a similar mode of reasoning to the spreads of higher multiplicities on 
S n _ v The spreads S n _ 2 , S n ^, . . . are developable, but 2„_ 2 , 2„_^, . . . arc 
not developable. 

5. Special case where the parameter enters rationally. 

Let us illustrate this theory by the case of the developable which is 
the envelope of the (« — l)-flat, 

a t m + mb r- 1 + i m (m — 1 ) c P~\ -f . . . . = 0, 



where t is a variable parameter, a, b, c, . . . are linear functions of the 
coordinates that are not expressible in terms of any v linear functions of 
the coordinates where v < n, and m is an integer which is not less than n, 
the number of ways of the space. Two consecutive F^s intersect in 
the F n _ 2 , 

ar -i + (m _ j) br -2+ O- 1 ) ' | m ~ 2) c r- 8 + . . . . + e = 0, 

- 1 

bf a ~ 1 + (m — 1) ct m ~ 2 + . . . + et +f= 0. 

The elimination of the parameter from these equations gives the equa- 
tion of S n _ v The result is the discriminant of the original equation 
placed equal to zero ; the order of *S'„_ 1 is then 2 (m — 1).* 

Three consecutive F n _^s intersect in the F n _& 

a r~ 2 + (m — 2)b t m - 3 +.... = 0, 

bt m ~ 2 + (m — 2) c t m -' +.... + = 0, 

ct m ~ 2 + + et +/= 0. 

The equations of S n _ 2 are found by eliminating the parameter from these 
equations. The result is a restricted system equivalent to two inde- 
pendent equations ; the order of the system, i. e., the order of S n _ 2 is 
3 (m- 2).f 

Similarly k consecutive F n _^s intersect in the F k , given by the k 


a fn-*+i + (m — k+ 1) b t m ~ k +....= 

b r- &+1 + (m — h + 1) c r~* +.... = 

+ 0*+/=O. 

The elimination of the parameter from these equations gives a 
restricted system equivalent to k — 1 independent equations, the equa- 
tions of S n _ k+y The order of S n _ k+l is seen to be (k + 1) (m — k). 

Lastly the intersection of n consecutive F n _^s is the point, F , given 
by the equations, 

a r-" +1 + (m — n + l)b t m ' n +.... = 

b r- n+1 + (m — ii+l)c t m ~ n +.... = 

+ et+ f=0. 

* Salmon, Higher Algebra, art. 105. 

t This is the condition that the three equations have a common root ; Salmon, 
Higher Algebra, art. 277. 



The elimination of the parameter from these equations gives a re- 
stricted system equivalent to n — 1 independent equations, the equation 
of S x whose order is n (m — n -f 1). 

We can find the equations of those exceptional points where n -f- 1 
consecutive F n _ x s intersect in a point, if we eliminate the parameter from 
the n + 1 equations 

a t m ~ n + (m — n) b m ~ n - 1 +.... = 

b t" 1 -" + O — n) c'"-"- 1 + .... = 

+ et + f=0. 

The result is a restricted system equivalent to n independent equa- 
tions; it is of order (n + 1) (m — n), which is the number of such 
points, cusps on Si. We may verify this result by forming the resultant 
of these (« + 1) equations. If we eliminate the variables from these 
equations we have a determinant of order n + 1. If we expand this 
result t enters to the degree (n + 1) (m — n) so that there are (n + 1) 
(m — n) values of t tnat cause this resultant to vanish. These values of 
t give the special points in question.* 

Any double point on S n _ x must lie on two i^_ 2 's. We may find the 
equations of the total double spread on £„_!, by expressing the conditions 
that the equations of an F n _ 2 regarded as equations in the parameter, 
have two roots in common. These conditions are t 

a, (m - 1) b, i ^j '- c, 



('» - 1) 


b, (m — 1) 


(m — \)e,f 

* For n — 3, these results agree with those of Salmon, Geometry of Three 
Dimensions, p. 296. Neither the results there nor these hold when the system has 
stationary (n — l)-flats. 

t Salmon, Higher Algebra, art. 275. 


where there are 2 (m ■— 2) rows and 2 m — 3 columns. This restricted 
system is of order | (2w — 3) (2 m — 4). The double spread repre- 
sented by these equations consists of two distinct parts, S n _ 2 and 2 n _ 2 . 
The order of 2 n _ 2 must be, 

J (2 m — 3) (2 m — 4) — 3 (m — 2) = 2 (m — 2) (m — 3). 

A triple point on S n _i must lie on three F n _ 2 's. We may find the equa- 
tions of the total triple spread on S n _ 1 by expressing the conditions that 
the equations of the F n _ 2 have three common roots. These conditions 
are expressed by means of a rectangular system similar in form to (I), 
in which however there are only 2 (m — 3) rows and 2 m — 4 columns. 
The order of the restricted system is 

~ (2 m - 4) (2 m-b) (2 m- 6). 

This triple spread consists of two distinct parts, S n _ 3 and 2 n _ 3 . The order 
of 2„_ 3 must be 

1 2 

-^(2m-4) (2m-5)(2m-6)-4(m-3)=-(m-3)(m-4)(2m-l). 
o I o 

In like manner we can find the equations of the total &-tuple spread 
on S n _ u by expressing the conditions that the equations of the JF n _i have 
Jc roots in common. These conditions are expressed by means of a 
rectangular system similar to (I), in which, however, there are only 
2 (m — k) rows and 2 m — h — 1 columns. This is a restricted system 

equivalent to k independent equations, of order -r~j (2 m — k — 1) 

(2 m — h — 2) . . . . (2 m — 2 k). This spread consists of two parts, 
S n _ k and % n _ k \ the order of the latter is 

JL (2 m — k—\)(2m-k-2) (2 m — 2 k)- (k + 1) (m — k). 

The total (n — l)-tuple curve on #„_! is given by means of a restricted 
system similar to (I), in which, however, there are only 2 (m — n + 1) 
rows and 2 m — n columns. We have then a restricted system equiv- 
alent to n — 1 independent equations whose order is 

(2 m — n) (2 m - n — 1) . . . (2 m - 2 n + 2). 

(n - 1) 


The order of the curve 2 is, 

— - (2 m — n) (2m — n — 1) (2 m-2n + 2) — n (m — n+ 1).* 

(n — 1)1 

The equations of all the w-tuple points on S n _ x are given by means of 
a rectangular system similar to (I), in which, however, there are only 
2 (jn — n) rows and 2 m — n — 1 columns. They form a restricted 
system equivalent to n independent equations, whose order is 

—. (2 m — n — 1) (2 m — n — 2) . . . . (2 m — 2 m) ; 
n ! 

this is the number of w-tuple points. The number of the rc-tuple points 
other than the cusps on S x , are 

— (2 m — n — 1) (2 m — n — 2) . . . . (2 m — 2 n) — (n + 1) (w — n). 

These points necessarily lie on Si ; they are either n-tuple points on 2i, 
or else they are n-tuple points on the combined curves Si and 2i. In 
three-fold space the double curve on the developable may have tripl 
points on it ; it can have no double points off of the cuspidal curve. 

If m = n, then the order of S x is n, and there are no cuspidal points 
on the curve ; this is the rational normal curve of Veronese. f The 
order of S n _ x in this case is 2 (n — 1) ; no developable S n _ x can be of 
lower order unless it is a cone or conoid, for no curve of lower order 
than n can lie in the n-fold space without at the same time lying in a 
space of fewer than n ways. 

Let us consider the case where m = p < n, where p is an integer. 
Any p -\- 1 consecutive F n _i& intersect in an F n _p_i whose equations are 

. A 9 A n 9 p A . 

If we use two homogeneous parameters X and /x instead of the single 
parameter t, these equations may be written 

* For n = 3, this result agrees with that in Salmon, Geometry of Three Dimen- 
sions, p. 296. 

t Veronese, loc. cit. 


in which form the parameter do longer appears. Any p -f 1 consecutive 
i^_i's intersect in the same F n _ p _ 1 as any other consecutive p -f 1 ; 
i. e., all the -F n _i's of the system contain the same F n _ p _ x . Any p-flat 
that does not meet this F n _ p _ l cuts S^_ x in a developable (p — l)-spread 
of order 2 (p — 1). This developable (p — l)-spread of order 2 (p — 1) 
lying in a p-flat is exactly similar to the case in n-fold space where 
m = n. The curve at the base of this system is of order p ; it is the 
rational normal curve of p-fold space. Hence we may derive this system 
by joining by lines all points of a developable (p — l)-spread of order 
2 (p — 1) in a p-fold space, to all points of an (n — p — l)-flat that does 
not meet the p-flat that contains the (p — l)-spread. S n _ 1 is a conoid 
of (n — 2)-flats with an (n — p — l)-way head. The generating F n _ 2 's 
of S n _i arise from the junction of the (« — p — l)-way head with the 
generating (p — 2) -flats of the (p — 1) -spread. The generating F n _ s 's 
of S n _ 2 arise from the junction of the (n — p — l)-way head with the 
system of generating (p — 3)-flats of the (p — 2)-spread, and so on. 
Any conoid ruled by a 1-fold infinite system of <?-flats with a (q — l)-way 
head is a developable spread, but not so if it has only an r-way head 
where r < q — 2. The latter spread is a developable only when the 
consecutive ^-flats have (q — l)-way intersection. Any conoid ruled 
by a 1-fold infinite system of (n — 2)-flats that have an (n — 3) -flat in 
common is a developable, but if they have only an (n — £)-flat in com- 
mon where k < 4, the conoid may or may not be developable. The 
cones and conoids with a 2-fold infinite system of generators are not 
developables at all. 

The points of intersection of two consecutive generators are not in 
general points of intersection of three generators. The equations of 
a generator may be written 

e+(m - 1)d+ (*'- i y™- 2 > c+ — o, 

/+(m - 1)c + ("- 1 H°'- 2 ) rf+ .,.. = o. 

The points of intersection of three generators of the system are given 
by the equations 



(m-l) (m-2) 
e, (m — 1) d, c, 

e, (in — 1) of, 

Q - 1) Qi» - 2) 
/, (m — l)e, g- -f/, 

= 0. 

/, O - 1) «f • 

where there are 2 (m — 2) rows and 2 m — 2 columns 
For t = we have the particular (n — 2)-flat 

e = 0,f=0. 

The next consecutive generator has for its equations, 

e + 8t . d= 

The intersection of the two consecutive generators is the (n — 3)-flat 

whose equations are 

e = 0, /= 0, d= 0. 

This F n ^ does not generally lie on the total triple spread for one of the 
equations of that system, namely 

(m — 1) (m — 2) c 

(m — 1) d, 

(m — 1) (m - 2) d, 
(m — 1) e, 


= 0. 

is not generally satisfied when the equations of the i^,_3 are satisfied. 

The points that satisfy both these systems of equations are evidently 
points on two consecutive generators and at the same time points on 
three generators. 



If there is a linear relation between f, e, and d, then these two consec- 
utive generators intersect in an (n — 2)-flat, i. e., they are coincident 
and we have a stationary generator of the system. If 


« = 0, 

is the equation of a stationary generator of the system. The equation 
of the developable S n _i in this case is 

(— 1H—2), 




0>d , (B> -l)( w -2) c 





"We see that / is a factor of the left member of this equation. When 
this factor is thrown out, the residual or proper developable is of a 
degree less by one than before. The orders of the multiple loci pre- 
viously given are also reduced, they only holding when there are no 
stationary ^_ 1 , s in the system. By means of Veronese's formulae we 
see that when there are /3 stationary F„_,'s the order of the A-way 
developable is reduced from (m — X + 1) (m — n -\- X) to (?i — A -f- 1) 
(m — n + X) — (n — X) (3. 

6. Tangent flats to a ^-spread where 2 < p. 

a. Definitions. 

We have treated up to this point the various developables that arise 
from a curve in ra-fold space. We shall show now that similar develop- 
ables do not arise from the consideration of the tangent flats of spreads 
of more than one way. 




be the equation of an (n — 1) spread of order m. We shall use the 
points (1), (2), A (1) + fi (2) to denote the points whose coordinates 
are x x , y x , . . . w x , x 2 , y 2 , . . . w 2 , and \ x x -{- p x 2 , \y x -\- py., , . . ., 
Xw x -j- \iw 2 , respectively, so that A (1) + ft (2) represents a point on the 
line (12), i. e., the line joining (1) and (2). We denote the result of 
substituting the coordinates of the points (1) or (2) in U by U x , and U 2 
respectively. We use the symbols 

( 9 9 9 \ T t 

A 2 U x = x, - h y, -, h • • • + »i n — U x , 

V 9 Xi 9x x die J 

( 9 9 9 \ 

A U = [x 2 — + y 2 7 r- + . . . + w 2 ^—) Uj 
\ a x 9 y dw) 

f 9 9 9 \ rT 

A U 2 =[X yr— + ^ h • . • + «> ^ Us, 

\ 9x 2 9y 2 9w 2 J 

(9 9 9 \ k 

^ k 2 U x ~(x 2 ^ h y 2 ■= h • • • + «>2 s — tfi- 

\ 9x x J 9y x <9wv 

In the last case the operator is to be applied h times to f^. Now 
A (1) + /i (2) is a point on the line (12), if it is also a point of the 
(n — l)-spread, it must satisfy the equation of the spread. Substitute 
the coordinates of A (1) + p (2) in Z7and we have 

A"' U x + A- 1 M A 2 U x + ^ T /i - A 2 2 0i + . . . 

u" 1 

. . . + —. A 2 ra U x = 0. 
m I 

The m values of A: /u that satisfy this equation determine the m points 
where the line (12) meets the (n — l)-spread. If the point (1) lies on 
the spread then 

t7 1= =0. 

If the line (12) meets the spread twice at the point (1), then 

U x = 0, A 2 U x = 0. 


The equation of the locus of all the Hues that meet the spread twice at 
(1) is A U x = 0. 

From the analogy of three-fold space, this locus of lines is called the 
tangent (n — l)-flat to the (n — 1) -spread, at the point (1).* At each 
point of an (n — l)-spread there is in general a unique tangent (n — 1)- 

A ^-spread is given by the equations, 



a restricted system equivalent to n — p independent equations. In a 
similar manner the equations of the locus of all lines that meet the 
jo-spread twice at any non-singular point (1) are, 

A U x = 0, 

AV 1 =0 ) 

A W l = 0, 

Since these equations are linear we may select any n — p that are inde- 
pendent and the rest are superfluous. t We have then a ^?-flat which 
from analogy is called the tangent p-flat to the p-spread at the point (1). 
At any point of a ^-spread there is in general a unique tangent p-fl&t.t 

We define a tangent r-flat at a given poiut of the jo-spread where 
r < p as an r-flat that Jies in the tangent />-flat at that point and con- 
tains the point. If r > p, we define a tangent r-flat at a given point 
as an r-flat that contains the tangent ;>flat at that point. The locus of 
tangent lines then to a ^-spread is simply the locus of tangent p-flats to 
the spread. The locus of tangent planes, 3-flats, ...,(/> — l)-flats is 
this same locus. If then there are developables that arise from a 
jo-spread, where 1 < p their number is not so great as n — p — 1, for 

* This proof is given in Dr. Story's Lectures on Hyperspace. 

t Some of these equations may be satisfied identically ; this will be the case 
when (1) is a multiple point on any of the {n — l)-spreads, but not a multiple point 
on the p-spread. 

t Dr. Story, Lectures on Hyperspace. 


the tangent lines, tangent planes, tangent 3-flats, . . . , tangent jo-flats all 
have the same locus. The planes through two consecutive lines, the 
3-flats through two consecutive planes, etc., the ^>-flats through two 
consecutive (p — l)-flats all have this same locus possihly of a certain 

b. Intersections of consecutive tangent flats. 

We shall show further that (p -f l)-flats cannot in general be passed 
through two consecutive tangent p-flats, for such p-^&ts do not in general 
have (p — 1) -flats in common. Tangent ^o-flats at consecutive points 

of a j9-spread where 1 < p < - do intersect in points at least. Let 



a restricted system equivalent to n — p independent equations be the 
equations of the p-spread. Let 

P' = (x 1 , y', . . . ) and P" = (x r + dx', y' + dy', . . . ) 

be consecutive points of the spread. The tangent jo-flats at these 
points are 

9 x' 9 y' 

9 V 9 V 
dx dy 


A U" = A U< + x 

/<? 2 U' 9 2 U' \ 

\j* dx ' + w*js d ' + ■■■■)= "• 

{9 2 V 9 2 V \ 

All of these equations being linear, only n — p equations in each set can 
be independent. In general, 2 (n — p) equations for such a value of p 
have no common intersection. In the present case the resultant of any 
n + 1 equations of the combined systems vanishes for any consecutive 
points P' and P" on the ^-spread, so that no more than n equations of the 
combined systems can be independent. Hence tangent ja-flats at con- 


secutive points of a ^-spread intersect in a point at least. Tangent 
planes at consecutive points of a surface in w-fold space intersect at least 
in points. These tangent planes do not generally intersect in lines 
unless the surface lies in a space of three ways. Let us take p to repre- 
sent the tangent plane at any point P of the surface and take p', p", 
p'", ... to represent the tangent planes at the points P', P", P'", . . . 
consecutive points of an infinitesimal closed curve about P. If p and p' 
intersect in a line they determine a three-flat. If the consecutive tan- 
gent planes intersect in lines, then p" has a line in common with both p 
and p' and so p" lies in this three-flat. In a similar manner it can be 
shown that p', p", p'" . . . , all the tangent planes consecutive, to p lie in 
the same three-flat with it, i. e. a unicpue three-flat is determined at each 
point of the surface that contains the tangent plane at the point and all 
the tangent planes consecutive to it. Since however this three-flat is 
determined by any two of these tangent planes, the three-flats corre- 
sponding to P and P' any two consecutive points are the same. Take 
now any curve through P that lies on the surface. Since the three-flats 
corresponding to any two consecutive points of the curve are the same, it 
follows that the three-flats corresponding to all the points of this curve 
are the same. If we take a different curve through P the same thing is 
true of the points of it. The three-flats corresponding to all the points 
of these two curves are the same since they are all the same as the 
three-flat corresponding to P. From this it follows that the whole sur- 
face and all of its tangent planes lie in the same three-flat. Hence if in 
general all the tangent planes consecutive to any tangent plane of a 
surface lie in the same three-flat with it, then the whole surface lies in 
this three-flat. 

In the same way it may be shown that if in general all the tangent 
planes consecutive to the tangent plane at any point of a surface lie 
in the same four-flat with it that the whole surface lies in this four-flat. 
Hence in w-fold space not only do the consecutive tangent planes of 
a surface not intersect in lines, but all the tangent planes consecutive 
to any tangent plane do not lie in the same four-flat with it. 

c. The locus of the intersections of the tangent plane at any point 
of a surface with the consecutive tangent planes. 

In a four-fold space let the surface be given by 



a restricted system equivalent to two independent equations. The 
tangent planes at P' and P", any two consecutive points, have for their 

9W 9U> 

9 x 9 y' 

9 V 9 V 

9x' dy' 


L W , = AU , + x (^ dxl + J^L i W + . ..) + .. .. = <>, 

(9' 2 V 9 2 V \ 

A V" = A V + x ~ dx> + ^-p^ dy' + ....+.... = 

\9 x'~ 9 x' d y' I 

Let us take the first two equations in each set to be independent, then 
the rest are superfluous. Since P' and P" are points of the surface, 

U' = 
V =0 

U"= U' + ^jdx' + = 0, 

d x 

9 V 
V" = V + %^dx> + = 0, 


From these three sets of equations we derive 

(9 2 U' 9' 2 U' \ 

x [jx^ dx ' + 9*9y-< dy ' + ' ' ' 'J + * * • ' = °' 

(d 2 V 9 2 V \ 

x \9^ dx ' + d*w? d * + • • • ■) +■ • • • = °' 

9 J^dx> + .... = 0, 


9 V 

? rT rf a r' + .... = 0. 


These four equations are homogeneous in the five differentials dx', 
d i/', . . . We may take one of these differentials to be zero and 
eliminate the other four. We have 



9 2 U> 
; ^^ + y 

9x 12 
9 2 V 



1 + 9 

9 2 W 
9 x' 9 y' 

9 2 V> 


9x' 9y 



Jx 1 

7 + 



9 2 U< 
9 x' 9 y' 

9 2 V 
9 x' 9 y' 

9 2 U> 
9y' 2 
9 2 V> 


9 V 

= 0. 

This determinant and its derivatives vanish for the point P', therefore 
the locus is a quadratic three-way cone with its vertex at PL This 
cone is intersected by the tangent plane at P' in a pair of straight lines 
which is the required locus. If a point x, y, . . . , be taken on either of 
these lines, we have three independent equations just sufficient to deter- 
mine the ratios of the four differentials ; i. e., just sufficient to determine 
the consecutive point P", so that the tangent plane at this consecutive 
point will intersect the tangent plane at P' in the point selected. That 
these two consecutive tangent planes have no further intersection may 
be further shown by forming the equation of the plane that goes through 
their common intersection and through both the points P' and P". The 
equations of this plane are 

A" V .&U> - A" U' . A V = 0, 
A' V" .AU"- A' U" .AV" = 0. 

These equations in general represent a definite plane so long as P' and 
P" are not coincident. 

It would be of interest to examine the motion of the point of inter- 
section along these lines as the point P" circles about the point P', and 
to see whether at any time the consecutive tangent planes intersect in 
one of these lines. 

These lines are not inflexional tangents to the surface ; lines meeting 
the surface in three consecutive points do not generally exist in a space 
of more than three ways. For such lines would have to satisfy both 

A U> = 0, 
A V = 0, 


A 2 U> = 0, 
A 2 V = 0, 


These equations, however, in general have only the point P' counted 
a multiple number of times in common. In general, then, in a space 
of more than three ways a surface is so twisted that there are no lines 
that meet the surface three times at a given point. This proof is easily 
extended to a surface in a space of more than four ways. 

d. The spreads that arise by considering the junctions of the 
consecutive tangent flats. 

Consider now any surface in rc-fold space. Draw the 2-fold infinite 
system of tangent planes. Pass a four-flat through every two consec- 
utive planes and there is a 3-fold infinite system of four-flats, form- 
ing in general a seven-spread. Each four-flat is met by the infinity 
of consecutive four-flats in the same plane. We may pass six-flats 
through every two consecutive four-flats. There is a 4-fold infinite 
system of six-flats constituting a ten-spread. This system of ruled loci 
in no wise resembles the system of developables we derived from a 
curve. Starting with a surface we cannot derive a system of develop- 
ables in the same manner as when we start with a curve. The same 
is true if we start with any ^-spread where 2 < p. Only in case the 
©-spread lies in a (p + l)-flat do consecutive tangent p-flats intersect 
generally in (p — l)-flats; the only exception is in the case the w-spread 
is a curve. 

II. Loci derived from an (n — 2)-flat whose Equation 
involves a Single Arbitrary Parameter. 

7. Description of the loci. 

Let us consider next the system of loci represented by an {n — 2)- 
flat whose equations involve a single arbitrary parameter. The parame- 
ter may enter rationally or irrationally. If it enters rationally we 

suppose it to enter to as high a degree as - iu each equation. Let the 

equations of the flat be 

.4 = 0, .5=0. 

In these equations we suppose further that the linear function of the 
coordinates that appear as coefficients of the various powers of the param- 
eter cannot be expressed in terms of fewer than n + 1 linear functions 
of the coordinates. Eliminate the parameter from these equations and 


we derive the equation of an (ti — l)-spread S n _ v which is ruled by the 
system of (n — 2)-flats, F n _ 2 s.* 

Two consecutive F n _ 2 's intersect in an (?i — 4)-flat, whose equations 

^ = 0,^ = 0^=0,^ = 0. 

The elimination of the parameter from these equations gives a re- 
stricted system equivalent to three independent equations. The locus is 
an (n — 3)-spread ruled by the F n _f&. S n _s is a double spread on S^_ x . 
Three consecutive F n _ 2 's intersect in an (ti — G)-flat F n _ 6 , whose equa- 
tions are, 

. 9 A 9" A 

A = °>-9^ = °> 9X>=°> 

9B_ 9*B_ 

If we elimiuate the parameter from these equations we derive a 
restricted system equivalent to five independent equations. The locus 
is an (n — 5)-spread S„_ 5 , ruled by the F„^s. S n _ 5 is a triple spread 
on S n _ 1 and a double spread on S n _ s . 

Similarly r consecutive F H _ 2 s intersect in an (n — 2 r)-flat F n _ 2r , whose 
equations are, 

A A 5 A A 9 r ~ 1 A A 

„ A 9B A 9 r - x B A 

On the elimination of the parameter we derive a restricted system equiv- 
alent to 2 r — 1 independent equations. The locus is an (« — 2 r + 1)- 
spread, S n _ 2r + V ruled by the F n _ 2r , s. S„_ 2r + i is an r-tuple spread on 
aS^j ; it is a multiple spread on other spreads of the system. 

Two distinct cases arise according as n is odd or even. If n is odd, 

n — 1 

then — - — consecutive F n _ 2 s intersect in a line, F 1} whose equations are, 

* From now on we shall use S k to denote the ^-spread of this system. 


. . 9 A 9^'A n 

^ = 0,^ = 0,.. .-==,= 0, 

B ft 3B -a ^ B ft 

B - 'ax- '--- s -T¥-°- 

If we eliminate the parameter from these equations we derive a 
restricted system equivalent to n — 2 independent equations. The locus 

is a surface S 2 ruled by the F x 's ; it is an ( — - — j-tuple surface on aS^. 

Consecutive i^'s do not in general intersect for the n -\- 1 equations 


^ = o,|i = o ; . 

n— 1 

9\ 2 

B=0, 3 ,f=0,. 

a A 


9* B 

a— i 
5 A" 2 " 


have not in general any common solutions. If we regard these n -f 1 
equations as homogeneous in the n + 1 coordinates and form their result- 
aut, the values of the parameter that cause it to vanish will give points 
where consecutive lines meet. The equations of these points may be 
formed by eliminating the parameter from the n + 1 equations, which 
gives a restricted system equivalent to n independent equations. These 

points are double points on S 2 and ( — - — j-tuple points on S n _ x . 

If n is even then — consecutive F n _ 2 '$ intersect in a point F , whose 

equations are, 

. n 9 A 9**A A 

A = 0, -=- = 0, . . . , — -j= 0, 


5 A" 

n = 2 

5 = 0,^ = 0,. ..,^=0. 

° A 9 A 2- 

The elimination of the parameter from these equations gives a restricted 
system equivalent to n — 1 independent equations. The locus is a curve 



Si, which is an [ - J-tuple curve on S n _i. There are not in general sta- 
tionary points on >$i, for the n + 2 equations 


.9 A 9' 2 'A 

A = 0, ^— = 0, . . . , — ^r= 0, 


9 A" 2 

3 i? 5~ 2 i? 
R— -— — - — — 


9 A 

have not in general any common solutions at all. 

If the equation of the (u — 2) -flat involve k parameters connected by 
h — 1 equations, the properties of the derived system of loci is the same 
as in the case just discussed. 

8. Mutual relations of the derived loci. 

Two consecutive F n _ 2 s intersect in an F n _ v three in an F n _$, r in an 

71 • 1 71 

F n -o_ri — 5 — m aD -^ij ^ n ' s odd, or - in an F if n is even. There is a 

1-fold infinite system of each kind of flats. The F n _ 2 s are generators 
of S n _i, the F^s of *S„_3, the F n __ 2r J s of «S^_ 2r+1 . Let us consider the 
case where rc is odd. Through any F n _ 4 pass two consecutive F n _ 2 s, 

n — 1 

through any i ?T „_ 2r pass r consecutive F n _ 2 's, through any F x pass — - — ■ 

consecutive F„_ 2 s. Any F n _ 2 contains two consecutive i^ n _4's, three con- 

n — 1 

secutive F n _QS, — - — consecutive i^'s. Any F n _ 2r contains two consecu- 


tive F n _ 2{r+1) , s, any two consecutive i^_ 2r 's determine one -^,_ 2 ( r _i)'s. We 
may then reverse the process and start with S. 2 , which lies in the space 
of n ways but in no flat space of a less number of ways. Through each 
two consecutive FiS of this surface pass three-fiats F s 's, these F 3 's will 
generate a four-spread S„_ 4 . Through each two consecutive F 3 's pass 
five-flats ; this can be done as the i^_3's intersect consecutively in i^'s. 
These five-flats will generate a six-spread S 6 . Finally, through each two 
consecutive F H _Js> pass F n _ 2 s ; these F n _ 2 s generate an (n — l)-spread 
S n _ i . If we start with the system of (n — 2)-flats we come down finally 
to the surface, or starting with the surface we may work back to the 
system of (ti — 2)-flats. 

If n is even, through any F n _± pass two consecutive F n _ 2 s, through any 


F n _ 2r pass r consecutive F n _ 2 s, through any F pass - consecutive F^_ 2 s. 


Any F n _o contains two consecutive F„_ 4 's, three consecutive i^„_ 6 ' s > o con- 

secutive FqS. Any F„__ 2r contains two consecutive -^ fT n _ 2 (r+i)'s and any 
two consecutive I , n _ 2r , s determine one F H _ 2{r _i ) except in the case that 

r = -. We cannot then start with a curve and retrace our steps ; two 

consecutive points of the curve Si do not determine uniquely a plane of 
the system. The i'Vs of the system in general intersect consecutively 
in the points of S v Starting with such a system of planes we may 
retrace our steps. Through any two consecutive planes of the S a we 
may pass a four-flat. These four-flats are generators of S 5 . Through 
any two consecutive B^s we may pass six-flats ; they are the generators 
of S 7 . Finally through any two consecutive i^_ 4 's pass (n — 2)-flats ; 
they are generators of S n _ t . We may retrace our steps only in case we 
do not begin with S v 

9. Director curves of the ruled (n — \)-spread. 

Let the equation of such a ruled (n — l)-spread S n _ x be 

= 0. 

"We shall show that the equations of the generating flats of the spread 
may be represented by linear equations involving a single parameter. 
The equation in homogeneous coordinate of an arbitrary (?i — 2)-rlat in 
n-fold space may be written 

x = a x z + fix «+.... + 71 w 

y — a 2 z + /? 2 s + . . . . + 72 w - 

In this form the equations of the (n — 2)-flat, which we may call the 
(n — 2)-flat AB, involve 2 {n — 1) independent arbitrary parameters. 
These parameters must be connected by 2 (n — 1) — 1 equation to make 
A B a generator of such an (n — 1) -spread. We wish to connect these 
parameters in such a way that A B will be a generator of the S n _i in 
question. The equations of a curve on <£ are 

<£ = 0, Ui = 0, u 2 = o,... u n _ 2 =o. 

If we eliminate the coordinates between these equations and the equa- 
tions of A B we derive a single equation in the 2 (n — 1) parameters. 
This resulting equation is the necessary and sufficient condition for A B 
to meet the curve. In a similar way we may derive 2 (« — 1) — 1 
such conditions and make -A B meet 2 (n — 1) — 1 curves on </>. If 
from these 2 (n — 1) — 1 equations and the equations of A B we elimi- 


nate the parameters, we derive a single equation in the variables alone. 
It is the locus of all the (n — 2) -flats that can be drawn to meet the 
curves in question, and so it necessarily includes all the generating flats 
of <jf>. It includes possibly other flats besides the generators of <j>, but in 
this case the general locus will break up into several components, and one 
component is <£. This is the case in three-fold space. 

The spreads U^ U 2 , . . . U n _ 2 may in each case be taken to be flats ; 
then the director curves are plane curves. These are the director curves 
of <£; any or all of these curves may be plane, or they may be twisted to 
any extent permitted by the space. Any 2 n — 3 curves in w-fold space 
may be taken as the director curves of a ruled (n — l)-spread. In three- 
fold space any three curves plane or twisted may be taken as the director 
curves of a ruled surface. In four-fold space, any five curves plane or 
twisted may be taken as the director curves of a ruled three-spread. In 
this case the generating planes intersect consecutively in the points of a 
sixth curve; so in four-fold space any five curves completely determine a 
sixth. In five-fold space seven curves plane or twisted may be taken as 
the director curves of a four-spread ruled by three flats. In six-fold 
space nine curves determine a five-spread ruled by four-flats. Consecu- 
tive four-flats intersect in planes and these in turn intersect consecutively 
in points. So in six-fold space nine curves determine a tenth. 

10. Multiple loci on the ruled (n — V)-spread. 

Any generator of the (ii — l)-spread is an (n — 2)-flat F n _ 2 \ it is met 
by any other generating F n _ 2 in an (n — 4)-flat. If then 4 < n every 
generator is met by every other generator. If n = 3, any generator is 
met by only m — 2 other generators, m being the order of the surface.* 

For 4 < n, any F n _ 2 contains a single infinity of (n — 4)-flats where it 
is met by the other F n _ 2 s. These are evidently double flats on &„_!• On 
&„_! there are in general a 2-fold infinite system of such (n — 4)-flats 
constituting a double (?i — 2)-spread, 2„_ 2 on S n _x. In general, then, any 
(n — l)-spread S n _ x ruled by (n — 2)-flats F n _ 2 s has on it such a double 
(n — 2)-spread 2„_ 2 ruled by the 2-fold infinite system of (n — 4)-flats. 
2„_4 has on it all those (n — 4)-flats, F^s that arise from the intersec- 
tion of consecutive i^,_ 2 ' s - These i^./s generate S n _s, which therefore 
lies on 2 n _ 2 and forms but an infinitesimal part of it. 

Any three F n _ 2 s intersect in an (n — 6)-flat; there are in general 
a 3-fold infinite system of such (n — 6) -flats constituting an (?i — 3)- 

* Salmon, Geometry of Three Dimensions, p. 427. 


spread 2„_3, a triple spread on S,^. S n _ 5 lies on 2„_ 3 , and constitutes 
but an infinitesimal part of it. If n is sufficiently great there is a quad- 
ruple (n — 4) -spread 2„_ 4 ruled by the 4-fold infinite system of (n — 8)- 
fhits arising from the intersections of four F n _ 2 's. S a _ 7 lies on S n _ 5 . 
We can go on in this manner until we reach a limit due to the narrowness 

of the space. If n is odd we have finally an f — - — j-tuple ( — - — )- 

spread ruled by the f — - — Wold infinite system of lines that arise from 

n — 1 
the intersection of — - — generating i^ 4 _ 2 's. There may be further an 

( — - — j-tuple ( — - — j-spread made up of the ( — - — j-fold infinite 

system of points that are the intersection of — - — generating F^s, an 

fn + 3\ , fn — 3\ , , , , n — 3 , , , . „ . 

I — - — j-tuple I — - — j-spread made up of the — - — fold infinite 

system of points that are the intersections of — - — generating -F„_ 2 's, 
etc., but these spreads do not always occur. In special cases the 2„_ 2 , 
or some component of it, may be of greater multiplicity than — - — • 


In three-fold space a ruled surface generally has on it a double curve. 
This double curve, or some component of it, may, however, be of 
greater multiplicity than two. It is to be observed that S n ^ lies on 
2„_ 2 . In three-fold space this means that consecutive generators of a 
ruled surface, if they intersect at all, must intersect in points of the 

double curve. If n is even we have finally an ( - j-tuple ( - j-spread 

2 n that is made up of the ( - j-fold infinite system of points that 


arise from the intersection of - generating F n _.?s. There may be an 

I - + 1 j-tuple f - — 1 j-spread 2„ whose points are points of inter- 

section of - + 1 generating i^,_ 2 's, an ( - + 2 j-tuple ( - — 2 j-spread 


2 n whose points are points of intersection of - + 2 generating F n _ 2 's, 

etc., though these spreads may not always be present. 


11. Special case where the parameter enters rationally. 

Let us consider the special case where the parameter enters rationally. 
Let the equation of the generating (n — 2)-flat F n _ 2 be 

A = a t l + b t 1 ' 1 + c t l ~ 2 + = 0, 

B = a' r + b' r _1 + c> r~ 2 + .... = o, 

where a, b, c, . . . , a', b', c', . . . , are linear functions of the coordinates 
that cannot be expressed linearly in terms of fewer than n + 1 linear 
functions of the coordinates. If we eliminate the parameter from these 
equations, we have the equation of the £„_! ruled by the -F„_ 2 's ; it is of 
order I -\- m. It is more convenient in what follows to use two param- 
eters, A and fx, that enter homogeneously into the equations. 

Two consecutive generators intersect in the F n _ 4 whose equations are 

9 X 9 jx 9 X 9 /x 

The elimination of the parameter from these equations gives a re- 
stricted system equivalent to three independent equations the locus is 
£ n _3, whose order is 

2 {I— 1) + 2 (m— 1) = 2 (Z+m — 2). 

The order is found by expressing the conditions that the four equations 
have a common root. The locus of the intersections of three consecu- 
tive F n _ 2 's is a locus of F„_ e 's ; the equations of this locus are found 
by eliminating the parameters from the equations, 

3"-A ^L_ 3M_ 
ix a [x 

9 A 2 ' ' 9X9fx ' 9r 2 

9 2 B _ 9 2 B 9 2 B _ 

9X 2 ~ ' 9\9fi~ ' 9fx 2 ~ 

This gives a restricted system equivalent to five independent equations ; 
it represents S n _s, whose order is 3 (I + m — 4). 

The r-tuple spread S n _ 2r+i on £„_! is represented by the equations that 
result from eliminating the parameters from the equations, 

9" A r*A 3^ 

ir-1 — U > CI vr-2 Cl .. — U ' * • * ' O ..r-1 U > 

9X"' 1 " ' 9k r ~ 2 9fx ' ' * "'5 


9 r ~'B 9 r ^B 9r ~ 1]3 -o 

9X^ ~ ' 9x r ~ 2 9,x - u ' • • • ' ^ " 


The equations then are of S n _o r+1 form a restricted system equivalent 
to 2 r — 1 independent equations whose order is r (/ -f- m — 2r + 2). 
As we have seen, there are two cases according as n is odd or even. 

If n is odd we come down finally to an f — - — J-tuple surface S. 

The equations of S 2 are found by eliminating the parameters from the 

n-3 n-3 n-3 

9~*'A _ 9'*' A 9~*'A 

n = 3 — ^' n-5 — O, . . . , n _ 3 — 0, 

9X' 2 ' QK'V'Qfi d/i r 

n-3 n-3 n-3 

n-3 — ^, n-S — "»•••} n-3 — 0. 

2 A" 2 "" , 9\'* dp 9fi Y 

The equations of $ 2 form a restricted system equivalent to n — 2 inde- 

n — 1 

pendent equations, whose order is — - — (I + m — n 4-3). 


There are also f — — J-tuple points jP 's on S n _ u though in general 

n 4- 1 

— - — consecutive F n ^ 2 's do not intersect. If we form the resultant of 

the n -f- 1 equations 

n-l n— 1 

5 2 ~J rt 9^'A 

—^i = 0, — ^ = 0, . 

3 A 2 9 k 2 9 ft 

n—l n—1 

5A. 2 3 A. 2 5 //. 


J w-l - 

= 0, 


9'^ B 

3/x 2 

= 0, 

we have a determinant of the (w + l)-st order, in which the parame- 
ters e 
n + 1 

n 4- 1 
ters enter to the degree — — — ( l 4- m — n -\- 1). There are then 

(I + m — n -\- 1) valujs of the parameters that cause this 


determinant to vanish, and so this is the number of points F . We 
can find the equations of these points by eliminating the parame- 
ters from these «4 1 equations. The result is a restricted system 
equivalent to ii independent equations. The order of the system is 

ii 4- 1 
— - — (I 4- m — ii 4- 1). This is another proof of the number of 

points F on S n _i. 



In case n is even we have finally the f — J-tuple curve whose equations 
are found by eliminating the parameters from the equations, 


3-~ A 

n-2 — 

2 A" 2 



o» -^— = o, . 

9\ 2 '9/x 



• • 5 n-2 — U J 
5 fX.' 2 




9 k 2 ' 

n 9^' B 

o, n < = o, . 

5a 2 9 /ji. 

9 ft 2 


The order of the restricted system is - (I + m — n + 2), the order 

of 8 V . 

We find the equation of the double spread 2„_ 2 on *S'„_ 1 , by imposing 
on the equations of the generating F n _ 2 the conditions that they have two 
common roots in the parameter. These conditions are,* 

a, b, c =0 

b, .... 




b', e', 
< V, 

where there are I -\- m — 2 rows and I -\- m — \ columns. This is a 
restricted system equivalent to two independent equations ; the order of 
the system is \ (J + m — 1) (I -\- m — 2). On 2„_ 2 must be S n _o. We 
find the equations of 2„_g by expressing the conditions that the equations 
of the generating flat have three common roots in the parameter.! The 
result is a restricted system similar in form to (II), in which, however, 
there are only I + m — 4 rows and / + m — 2 columns. This restricted 
system is equivalent to three independent equations, and its order is \ 
(I + m — 2) (/ + m -3) (1+ m — 4). 

The equations of 2„_ r are found by expressing the conditions that the 
equations of the generating (n — r)-flat have r roots in common. By an 
extension of the previous method we derive a restricted system of the 
same form as (II), in which, however, there are only I + m — 2 (r — 1) 
rows and I -\- m — (r — 1) columns. This is a restricted system equiva- 

* Salmon, Higher Algebra, Art. 275. 

tlbid., Art. 285. 


lent to r independent equations, the order of the system is — - (I + m — 

r ! 

r + 1) (Z + m — r) . . . . (Z -f m — 2 r -f- 2). 

Whether n is odd or even we have finally a curve 2i of multiplicity 
n — 1, whose equations are found by expressing the conditions that 
the equations of the generating (n — 2) -flat have n — 1 roots in the 
parameter in common. We derive a restricted system of the same 
form as (II) in which however there are I + m — 2 (n — 2) rows and 

I + m — (n — 2) columns. The order of this system is — 

V ; * (n - 1)1 

(Z+ m — n + 2) (Z + m — n + 1) . . . . (I + m — 2 n + 4). This curve 
has M-tuple points on it whose equations are fouud by expressing the con- 
ditions that the equations of the generating (n — 2)-flat have n roots in 
common. We again have a restricted system of the same form as (II), 
in which, however, there are I -\- m — 2 (« — 1) rows and I -f- m — n + 1 

columns. The order of this system is — - (I -\- m — n -\- 1) (I + m — n) 

. . . . (I + m . 2 n + 2), which is the number of points in question. For 

n = 3 these formulae for the order agree with those given in Salmon.* 

A very special case is where the parameter enters only linearly in one 

of the equations of the generating (n — 2)-flat. Let the equations of the 

flat be 

A = a t + b = 0, 

B = a' t m + V r- 1 + . . . . = 0, 

where we make the same suppositions regarding a, b, a', b', . . . , as 
before. The S a _ t in this case is a ruled spread with m sheets through 
the (n — 2)-flat, whose equations are 

a = 0, b = ; 

it has no other multiple locus on it at all. Consecutive generating -F„_ 2 ' s 
of the system intersect in the flat, whose equations are, 

9 B 
a = Q,b = 0,B= 0, V- = 0. 


All the F^s of the system lie in the same (« — 2)-flat ; they generate a 
developable (n — 3)-spread «S'„_ 3 in this flat. S' n ^> is the section by this 
flat of the developable (n — l)-spread enveloped by the (n — l)-fl;it B. 
Consecutive generating F^'a of S n ^ intersect in generating -F„_ 4 's of 

* Salmon, Geometry of Three Dimensions, p. 428. 


<S'„_3. By means of an (n — 3)-way developable lying in an (n — 2)-flat 
and two arbitrary curves we can generate a ruled (a — l)-spread by 
taking all the (n — 2)-flats that can be drawn through the enveloping 
(n — 3)-flats of the developable so as to meet both curves. 

We have seen that the section of an (n — l)-way developable by an 
(n — l)-flat gave an (?i — 2) -way developable of the same nature, so 
here the section of an (n — l)-spread ruled by (n — 2)-flats by an 
(n — l)-flat gives an (n — 2)-spread of the same nature as the (n — 1)- 

III. Loci derived from an (?i — &)-flat whose Equations 
involve a Single Arbitrary Parameter. 

12. Description of the derived loci. 

We shall complete the general theory by considering the locus of the 
1-fold infinite system of (n — &)-flats, where 2 < £ whose equations all 
contain a single arbitrary parameter. Let the k equations of the flat be 

A = 0, B = 0, . . . , G = 0. 

The equations of the locus of these i^^'s are found by eliminating the 
parameter from these equations. The result is a restricted system 
equivalent to k — 1 independent equations. 

The locus is an (n — k + l)-spread 5„_ HI ruled by the F„_ k 'a. Any 
two consecutive i^'s intersect in an (n — 2 £)-flat F n _ 2k whose equa- 
tions are 


If we eliminate the parameter from these equations, we derive a restricted 
system equivalent to 2 k — 1 independent equations. The locus is an 
(n — 2 k + l)-spread *S , „_ 2 i+i ruled by the F n ^ 2k s ; it is a double spread 
on S„_ k . 

Any three consecutive F n _ 2k 'a intersect in an (n — 3 £)-flat F n _ 3k whose 
equations are, 

The elimination of the parameter from these equations gives a restricted 
system equivalent to 3 k — 1 independent equations. Their locus is an 
(,a _ 3 h -}- l)-spread ruled by the F^-^s. S n _o k+l is a triple spread on 


The equations of the locus of the intersections of r consecutive F n _ k s 
are found by eliminating the parameter from the equations 

9 A 9^ A 


case we come 

This gives a restricted system equivalent to r k — I independent equa- 
tions. The locus is an (n — rk -f l)-spread ruled by the F tl _ rk %, it is an 
r-tuple spread on S n _ k+1 . 

There are k cases according as n = (mod k), n = 1 (mod £), . . . , 
n = k — 1 (mod k). In the first case we come finally to a curve S t 

which is an ( y- j-tuple curve on S„_ k+l . In the second 

down finally to a system of lines F^s which are generators of a ruled 
surface S 2 . In the last case we come down finally to a ^-spread ruled by 
(k — l)-flats. There are on S k in general special points where two con- 
secutive F k _i's intersect. 

13. Multiple loci on the spread; mutual relations of the system of 

S n -k+\ nas on it m general multiple loci that arise from the intersection 
of non-consecutive F n _ k s. Any F n _ k intersects every other F n _ k in an 
(n — 2 £)-flat ; there is in general a 2-fold infinite system of such 
(« — 2 £)-flats constituting a double (n — 2 k + 2)-spread 2„_ 24+2 on 
Sn-k+i- Evidently S n _ 2k+1 lies on 2 n _ 2fcf 2- Any three F n _ k 'B intersect in 
an (n — 3 £)-flat ; there is a 3-fold infinite system of such (n — 3 k)- 
flats, they constitute in general a triple (n — 3 k + 3)-spread 2 n _3 A . +3 on 
'S'n-A+i- S n _ Sk+1 nes on %n-sw Any r consecutive F n _ k 's intersect in an 
(n — r k)-i\at ; there is an r-fold infinite system of such (n — r£)-flats 
in general, constituting an r-tuple (n — r k + r)-spread 2„_ rjbfr on S„_ k+U 
on which lies S a ^ rk+V 

Finally the locus of the intersection of any a F n _ k 's where a is the 


greatest integer in T is an a-tuple [n — a (k — l)]-spread l n _ a ll _ 1) on 

<S tl -k+i ; it is ruled by the a-fold infinite system of (n — a £)-flats. 

The question arises, When, in general, do these double loci cease to 
exist? The double spread is in general an (n — 2 k -f- 2)-spread 2 n _ 2it+ 2. 
To have a continuous locus of double points we must generally have 


n + 1 


2 k + 2% 1 or £ ^ 

For values of k that satisfy this condition there is in general a continuous 
locus of double points. If 

rc-2&+2 = 0, ov k = ^i-= 

there is in general only a finite number of double points on the locus. If 

n — 2k+2<0,ork> n ^^- 

there are in general no double points on the locus. 

If there enter into the equations of the generating (n — £)-flat p 
parameters connected by p — 1 equations the properties of the system of 
related loci will be similar to those of the system just described. 

Any two consecutive F n _ k 's intersect in an F n ^ 2k while through any 
F n __< 2k pass two consecutive F„_^a. Any three consecutive F n _ k s intersect 
in an F n ^, k while through any F„_o k pass two consecutive F n _ 2k s and 
three consecutive F n _ k s. Any two consecutive F n _ rk s determine in 
general one F ll _ k(r _ l) . An exception may occur if r = a the greatest 

integer in -=• • Thus, if n = ^mod k), two consecutive points of ^ do 


not determine a (k + l)-flat where 2 < k. 

If n = 1 (mod k), two consecutive lines of S- 2 do not determine a 
(k + l)-flat, except in the case k — 2. In the last case, however, where 
n EE k — 1 (mod k), two non-intersecting (k — l)-flats do determine a 
(2 k — l)-flat. Only in this last case can we retrace the steps if we 
come down to the last spread. We can always retrace the steps if we 
do not come down to this last case. 

14. Director spreads of the ruled spread. 

The equation in homogeneous coordinates of any (n — £)-flat, 2 < k, 

may be written 

x = ai s + & t + . . . . + y x w, 

y = a 2 * + (3o t + . . . . -f y 2 w, 

z = a k S + (3 k t +.... + y k W. 

In this form the equations of the flat contain k (n — k -f 1) independent 
parameters. These parameters must be connected hy k(n — k + 1)— 1 
equations for this (n — £)-flat to be a generator of such a ruled 
(n — k -f- l)-spread. Any curve is given by the equations 


x = °, 

• t • • 

a restricted system equivalent to n — 1 independent equations. If we 
eliminate the coordinates between the equations of the flat and curve, we 
derive a restricted system equivalent to k — 1 independent equations in 
the parameters alone. These are the conditions that must be satisfied 
for the (n — &)-flat to meet the curve. In a similar way we may derive 
a restricted system equivalent to k — p independent equations in the 
parameters alone which are the necessary and sufficient conditions for 
the (n — &)-flat to meet a certain ^-spread where 1 < p < k — 1. We 
may have then curves, surfaces, . . . , or ^-spreads where 1 < jt> < & — 1 
for the director loci of a ruled (« — k + l)-spread. The numbers of loci 
of each kind that must be taken are A, p., ... v, p, namely, non-negative 
integers chosen to satisfy the equation 

A (k — 1) + ix (k — 2) + . . . . + v . 2 + p ■ 1 = k (n — k + 1) — 1. 

If we consider a group of one or more points as a director locus of the 
spread, we have to select integers to satisfy 

k . k + A (k — 1) + . . . . + p ■ 1 = k (n — k + 1) — 1. 

We may apply this to special cases. The director loci of a ruled surface 
in three-fold space are three curves. We may take one curve and a 
group of k points, in which case the ruled surface is reducible and has for 
its components k cones whose vertices are the k points and whose 
common base is the curve in question. In four-fold space the director 
loci of a ruled surface may be five surfaces, three surfaces and one curve, 
or one surface and two curves. The ruled surface in each case consist- 
ing of all the lines that can be drawn to meet all the director loci. In 
the same space the director loci of a three-spread ruled by planes may 
be taken to be five curves. 

If the director loci be all taken on any S n _ k+1 , then the locus of all the 
(n — £)-flats that can be drawn to meet these director loci will include 
as one of its components the S n _ k+ i in question ; it may or may not 
have other components. 

There are several special cases illustrative of these methods that can 
be worked out in still greater detail. Some of these I hope to make the 
subject of another paper. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVU. No. 6. — September, 1901. 


By O. II. Basquin 

With Two Plates. 

Investigations on Light and Heat made and published wholly oe in part with Appropriations 


By O. H. Basquix. 

Presented by C. R. Cross. Received June 8, 1901. 

The Problem. 

The arc spectra of those elements which are gases at ordinary tem- 
peratures and pressures have not been extensively studied. Their spark 
spectra, however, are easily obtained, and were among the first to be in- 
vestigated. The general impression prevails, therefore, that these ele- 
ments do not possess arc spectra. On the other hand practically all the 
so-called "hot stars" and all the "new stars" possess the more impor- 
tant lines of the hydrogen spectrum. Although our knowledge of what 
is going on in the arc and in the spark is very crude and unsatisfactory, 
yet it is, to the average mind, much easier to imagine a star as being in 
a condition similiar to that of the arc, rather than in one similar to that 
of the electric spark. It has seemed worth while, therefore, to search for 
the more important lines of hydrogen in the arc spectrum. This is the 
problem of the following investigation. 


Liveing and Dewar* examined the carbon arc in an atmosphere of 
hydrogen and saw "the fairly bright" C line of hydrogen, also "a faiut 
diffuse band " at the position of the F line of hydrogen. They obtained 
these two lines also by allowing small drops of water to fall into the arc 
in air.f They found the F line usually obscured by continuous spectrum, 
becoming visible at intervals only, when, from some variation in the work- 
ing of the arc, the continuous spectrum was less brilliant. Crew and 
Basquin t incidentally noticed these two lines of hydrogen while work- 
ing with the rotating metallic arc in an atmosphere of this gas. 

* Proc. Roy. Society, 30, 156 (1880). t Ibid., 35, 75 (1883). 

t Proc. Amer. Acad., 33, 18 (1898). 




In searching for these lines I have employed the rotating metallic arc » 
wh "h s'one to nse chemically pnre electrodes having httle or no 
rhemical reaction with the gas employed. In this arc, then, one my 
exne the gas to give off its characteristic radiations with greater m- 
ensi v han "n one where the gas may enter into chemtcal compounds 
W re a temperatnre is reached at which it becomes lum.nou. Tins ar 
enables one also to select snch metals as do not have strong hues m the 
neighborhood of the lines sought for, while in the spectrum of the carbon 
arc there arc few spaces not already ocenpied by lines of carbon or of an 

Tie rotating arc, one electrode, either a disc or a rod of meUjl 
rotates npon an axis, making abont 700 rotations per minute, while the 
o her electrode has a slow movement of translation toward U-».. f 
rotation The rotation not only prevents the excessive heating and 
weTdtng together of the electrodes, bat it throws the hot gases to one 
Tide o° thai the arc has the appearance of a small fan. The part of the 
tne tl separated from the poles is very free from continuous 

SP TnTe apparatus used in these experiments the arc is enclosed in a 
brass box or ■ « hood," having a volume of about 1* litres and being corn- 
el ivly .as-tight. The light from the arc issues through a long bras 
LTdosed with a lens at the outer end ; the lens thus forms part of the 
S of the hood, but is so far removed from the arc that it receives »m- 
parativel, little of the deposit sometimes formed inside the hood, and 

hence remains clean. lnnT , 0[! - f _ t 

A stream of gas enters the hood at one stop-cock and leaves ,t at 
another- a third cock is provided for nttachment to a manometer A - 
1th the hood is not absolutely gas-tight, the purity of the gas inside 
preserved in these experiments, partly by the small excess of pres- 
Tre i id tie hood above that outside, and partly by the fresh supply of 
; u e gas constantly running through the hood. The hydrogen used w 
generated electrolytically, and varied in quantity from 10 to lo hues 

^ThTspectra have been examined both visually and P» b ical,y 
by means of a small plane grating spectroscope and by means of a large 
concave grating spectroscope. 

* Crew and Tatnall, Phil. Mag., 38, 379 (1894). 


Observations of Hydrogen Lines. 

The arc spectra of the following metals in hydrogen have been ex- 
amined : Aluminium, copper, magnesium, coin-silver, sodium, tin, and 
zinc. With the exception of sodium the arc of each metal shows to the 
eye very clearly the H a and ILj lines of hydrogen, and in most of them 
the H ? line comes out with the small instrument very clearly, and in- 
distinctly with the large one. The H 5 line shows only rarely, and then 
to the eye rather indistinctly. The II a line is quite sharp and well de- 
fined, unless the electric current through the arc is unusually great ; it 
has much the same appearance as the zinc line at 6363. The other three 
are always broad, hazy, and ill-defined. 

On the photographs taken with the large spectroscope H^ and II V 
usually show very plainly, always excepting the spectrum of metallic 
sodium, while H5 shows in spectra of tin, silver, and copper. On 
photographs taken with the small spectroscope -these lines show more 
sharply, on account of the very much smaller dispersion, and the photo- 
graphs of tin show the next hydrogen line, H e quite clearly. Not hav- 
ing found the hydrogen lines in the metallic sodium arc (using copper as 
stationary electrode), I tried it in dry hydrogen also, thinking that in 
some way the water vapor might have affected the appearance of the 
hydrogen lines, but I have been unable to detect any of the hydrogen 
lines in that arc in any way. 

None of these lines excepting H a is sharply defined. A wide space 
in the middle of each line has fairly uniform intensity, shading off gradu- 
ally and uniformly to each side. The following table gives a rough 
estimate of widths, in Angstrom units, of these lines as they appear on 
the photographic plates, the middle of the shading being taken as the 
edfre of the line. 


H a 

H y 


II e faint, same general width. 

It will be noticed that these lines, with the exception of TT ai are exces- 
sively wide, and I think it is for this reason alone that I have been 
unable to photograph the still weaker hydrogen lines of Balmer's series. 

imum width. 



Mean width 














They may appear upon the plates, but are so wide and so faint that they 
cannot be detected upon the general shading of the plates. 

That these lines are not merely spark lines introduced into these arc 
spectra by the supposed spark at the breaking of tbe current through the 
rotating arc is shown, first, by the fact that they were first observed in 
the carbon arc, and, second, by the fact that I have seen H a and Hp quite 
clearly in the magnesium metallic arc, when the poles were not rotating. 
The lines produced in the stationary arc have much the same character 
as in the rotating arc, but there is a large amount of continuous spectrum, 
appearing as a background, in the case of the stationary arc, so that it 
would be difficult to photograph the hydrogen lines in this way. 

These lines in the arc seem to be due to hydrogen, and not to water 
vapor coming from the hydrogen generators.* This is shown by the fol- 
lowing two experiments : (1) I passed the stream of hydrogen through 
concentrated sulphuric acid and phosphorus pentoxide ; and even after the 
stream of dry gas had. been running through the hood for three hours, I 
found the H a line as bright as it was in the damp hydrogen coming 
directly from the generators. (2) In place of the current of dry hydro- 
gen, I passed through the hood a stream of air bubbling through warm 
water, so that this air was charged with moisture to about the same 
degree as the moist hydrogen coming directly from the generators. In 
this case I was not able to detect the faintest trace of the H a line. 
Magnesium poles were used in both the above experiments. 

Other Methods. 

I have examined some of these metals in commercial ammonia gas, 
such as is used in refrigeration. In this gas the hydrogen lines come out 
with nearly the same intensity as in hydrogen when copper or aluminium 
electrodes are used; no hydrogen lines are seen in the sodium arc in 
ammonia, although the arc works well, and when tin electrodes are used 
in ammonia a black dust collects in the atmosphere about the arc to such 
an extent as to shut off practically all the light within thirty seconds after 
starting the arc. From the standpoint of convenience and safety, the 
ammonia gas is much to be preferred to hydrogen. 

The copper arc in coal gas shows the H a line very clearly, but the 
other hydrogen lines are not distinguishable on account of the multitude 
of comparatively strong carbon lines which the coal gas furnishes in this 
part of the spectrum. 

* Trowbridge, Phil. Mag., 50, 338 (1900). 


Following the suggestion of Liveing and Dewar, above referred to, I 
have tried the rotating metallic arc in air, playing a very small jet of 
water upon the rotating electrode. In this manner the silver arc works 
rather more poorly than usual, and resembles a rapid series of small 
explosions. The hydrogen lines come out clearly, but are rather weaker 
and more diffuse than in the hydrogen atmosphere. 

The copper arc works well in an atmosphere of steam, much better 
than in hydrogen. The hydrogen lines are nearly, if not quite, as strong 
in steam as in hydrogen. The electrodes of the arc are slightly oxidized 
and have very beautiful colors. In making this experiment a slight 
alteration was necessary in the hood of the arc. The window through 
which the light issues is usually as far away from the arc as possible, but 
it was moved for this experiment so as to be as close to the arc as pos- 
sible. It was placed at the inner eud of a brass tube projecting into the 
hood, in order that the heat of the surrounding steam and hot air, as well 
as that of the arc itself, might prevent condensation of steam upon the 
surface of the window. 



Crew and Basquin * have sought to eliminate the radiations due to 
chemical causes in the electric arc by using chemically pure metallic 
electrodes and enclosing the arc in an atmosphere of hydrogen or nitro- 
gen. They interrupted the current through the arc about 110 times per 
second and examined the light of the arc while the current was null. 
They found in the rotating metallic arc in air " a luminous cloud " per- 
sisting for several thousandths of a second after the current through the 
arc had ceased, but they found no such luminous effect in an atmosphere 
of hydrogen or nitrogen. This seems to show that the cloud is due to 
chemical action going on in the gases after the electric current has 
stopped, and that in hydrogen the chemical action is too feeble to be 
noticed in this way. 

Liveing and Dewarf found a magnesium "line" at 5210, making its 
appearance in the arc spectrum only upon the introduction of hydrogen 
or coal gas into the arc. Professor Crew t gives a number of lines ap- 
pearing in the iron arc in hydrogen and not appearing in the arc in air. 

* Proc. Amer. Acad., 33, 18 (1808). 
t Proc. Roy. Society, 30, 96 (1880). 
t Phil. Mag., 50, 497 (1900). 


Hydrogen-metal Flutings. 

With the exception of tin, every metal thus far examined in the 
rotating metallic arc in hydrogen gives a characteristic set of spectrum 
Hues which are not found in the arc in air. Inasmuch as compounds of 
hydrogen with some metals are known, I have, in lieu of a better hypoth- 
esis, supposed that these lines are due to such compounds formed in the 
arc. No new isolated lines, surely due to hydrogen, have been found. 
The following description takes up the metals in the order of the relative 
intensities of these flutings. 


No fluting has been discovered due to a combination of tin and hydro- 
gen. There are four lines of intensity \ on Rowland's scale, at ap- 
proximately 3715, 3841, 4245, and 4386, which have not yet been 
identified. These may be weak tin lines not listed, or weak impurity 
lines. The deposit which is formed in the hood enclosing the arc is very 
small in amount and of a greenish color, and consists of very small 
globules. If this deposit is heated upon platinum foil in a Bunsen flame 
it quickly glows, and thereafter has a slate color ; and if this powder is 
placed in hydrochloric acid it dissolves when heat is applied and gives 
off bubbles of gas. If the dark powder, after the first heating, is reheated 
on foil in the flame, it glows again, apparently at a higher temperature 
than before, and then becomes a very white powder, both of which ex- 
periments go to show that the original powder is not metallic tin but is 
possibly some combination of tin and hydrogen. 

Coin Silver. 

This metal gives a delicate fluting with first head at 3333.86 and run- 
ning toward longer wave lengths. There are only about fifty lines in 
this fluting, and they have an average intensity rather less than h on 
Rowland's scale. 


This metal gives a rather open fluting, having the head at 4279.77 and 
running toward the longer wave lengths. The number of lines in this 
fluting is about sixty, and they are individually stronger than those of the 
coin-silver fluting. This fluting makes its appearance also when an 
atmosphere of ammonia or of steam is used. The deposit formed inside 
the hood is rather small in amount and of a brown color. The following 
table gives the wave lengths of the hydrogen-copper flutings : — 










Intensity. Remarks. 









ghost of 4275? 



















1 + 



1 + 





1 + 



2 hazy 






very indistinct, 




1 + 






1 + 







1 + 







slight shading toward 

























The aluminium arc in hydrogen gives a beautiful fluting with first head 
at 4241.26 and running toward longer wave lengths. This fluting ap- 
pears equally well in an atmosphere of ammonia. The following table 
gives the wave lengths and intensities of the principal lines : — 

lengths, ^tensities. 


lengths. Intensities. 




1st head. 






















4255 22 


4246 58 








wide, 2d head 



lengths Intensities - Remarks. 

lecths Intensities . Remarks. 








































impurity here. 




impurity here. 











3d head? 



















4372.54 • 
































impurity superposed. 

4th head. 

The magnesium arc in hydrogen gives the three flutings discovered by 
Liveing and Dewar * in the magnesium-hydrogen spark, with first heads 
at 5618, 5210, and 4849, and running toward the shorter wave lengths. 
The fluting at 5210, which is the cme showing the plainest on my photo- 
graphs, is made up of such very fine lines near the heads that the princi- 
pal head appears like a line by itself; but farther away from the heads the 
lines seem to become stronger and to overlap one another, so that many of 
these lines are much stronger than the head itself and their distribution 
seems quite irregular. I mention this more particularly because it is 
characteristic of the hydrogen-zinc and hydrogen-sodium flutings de- 
scribed below. I have noticed that in the spark, the intensity of the 
magnesium flutings is greatly increased with respect to that of the "b" 
group by the introduction of inductance in series with the capacity 

* Proc. Roy. Society, 32, 189 (1881). 


shunted about the induction coil. The deposit iu the hood enclosing 
the magnesium arc in hydrogen is quite plentiful, has a dark slate 
color, decomposes water at ordinary temperature, giving alkaline reaction, 
and oxidizes rapidly on heated platinum. 


The zinc arc in hydrogen gives a collection of lines between 4300 and 
4050, having an average intensity from 2 to 4, and not found in the arc 
in air. This appears to be a set of flutiugs of complicated structure 
having heads less distinctly marked than usual and running toward the 
shorter wave lengths. The semi-opaque deposit formed in the atmos- 
phere of the hood is so considerable that a current of not more than 
about four amperes can be used. This deposit is dark brown in color, 
gives alkaline reaction in water, but does not decompose it enough to 
form bubbles even when heated. It dissolves completely in sulphuric 
acid, forming a clear solution, and rapidly oxidizes on heated platinum. 


The sodium spectrum was obtained by using metallic sodium as the 
cooler rotating electrode and copper as the stationary one. As above 
mentioned, there is not the slightest trace of any of the hydrogen lines to 
be detected in this spectrum either visually or on the photographs, but 
there is a strong series of lines between 5000 and 3800, resembling the 
hydrogen-magnesium series in character. This is probably a complicated 
fluting of heads less clearly marked than usual and running toward the 
shorter wave lengths. A compound of sodium and hydrogen is already 
well known. The formation of the semi-opaque deposit in the atmos- 
phere of the hood is so considerable that the arc can be run only about 
five minutes at a time. I have not tried the sodium arc in air. 

The sodium spectrum obtained in hydrogen is itself quite interesting. 
All the sodium lines given by Kayser and Runge* come out very clearly, 
but the principal interest centres about the D lines, which are very in- 
tense, and so wide as to cover all the region between them. "When 
observed visually their reversals change in width quite rapidly. At first 
these reversals may be quite narrow black lines, and then they quickly 
widen and blot out the whole of the bright field between them. The 
width of the two lines taken together is about 150 Angstrom units, 
though the photographic plates are stained for a much greater width. 

* Kayser & Runge, Weld. Ann., 41, 302 (1890). 


The strongest copper lines show only very faintly, the weaker ones not 
at all. 

Correlation of Effects. 

In the metals arranged in the order given above (tin, silver, copper, 
magnesium, aluminium, zinc, and sodium) the following relations hold 
roughly : — 

(1) The set of lines characteristic of the spectrum of each metal in an 
atmosphere of hydrogen is stronger than that of the preceding metal of 
the series ; (2) the hydrogen lines appearing in the spectrum of the me- 
tallic arc of each metal are stronger than in that of the succeeding metal 
of the series ; (3) the general working of the metallic arc is worse for the 
metals at the first of the series than for those at the end. Briefly stated, 
the intensities of the hydrogen lines coming out in the spectra of various 
metals are roughly inversely proportional to the intensities of the char- 
acteristic flutings of those metals. 



Liveing and Dewar * found the carbon arc to work badly in hydrogen, 
and to give spectral lines of different relative intensities than in air. 
Professor Crew | has given quantitative measurements of the changes of 
intensities for the metallic arc spectra of magnesium, zinc, and iron. 

The general effects of the hydrogen atmosphere may be summarized 
thus : — 

(1) The arc works poorly in hydrogen. (2) The intensity of the 
whole spectrum is greatly reduced in hydrogen. (3) Those metallic lines 
which belong to the series of Kayser and Eunge are uniformly reduced 
in intensity. (4) Other lines are reduced in intensity but not uniformly. 
(5) Certain lines supposed to belong to the spark spectrum make their 
appearance in the arc in hydrogen. 


The radiations of the electric arc are generally admitted to be due to 
three causes, — electrical, chemical, and thermal. The chemical cause 
must depend upon the electrical cause in some way, for the chemical cause 

* Proc. Roy. Society, 33, 430 (1882). 
t Phil. Mag., 50, 497 (1900). 


cannot originate the arc, and the chemical cause follows the electrical in 
point of time, as is shown by the " luminous cloud " of Crew and Basquin 
above referred to. The thermal cause also must depend upon the electri- 
cal cause in some way. It probably depends upon it directly, but in any 
event, it is a function of it through the chemical cause, for all chemical 
reactions either take in heat or give off heat. 

Let us consider two arcs which are alike except that a larger current 
runs through the first than through the second. Since the secondary 
causes of radiation go hand in hand with the electrical cause we may 
expect the first arc to have a spectrum which is uniformly brighter from 
one end to the other than that of the second arc. With the exception of 
a slight variation probably clue to conduction losses, this is just what is 
always observed and confirms the secondary character of the chemical and 
thermal causes of radiation. If these causes were not dependent upon 
the electrical cause, we might possibly get an arc which would give only 
a flame spectrum or an arc which would give only a spark spectrum. 

Let us now suppose that we run the same current through both the 
similar arcs, and suppose that in some way we reduce the chemical action 
going on in the second arc. What difference may we expect to observe 
in them ? 

A reduction of the chemical action necessarily involves a reduction of 
the temperature of the arc, because the chemical reaction in the arc in air 
is exothermic, We have then an arc of lower temperature. If it is a 
stationary arc it will be shorter and will go out more frequently. If it 
is rotating it will have a smaller flame and work more poorly. All of 
which is amply verified by experiments in hydrogen. 

But we may expect this reduction of chemical action to have certain 
effects upon the spectrum. If all the lines of the spectrum of this arc 
were functions of the electrical cause alone, then there would be no re- 
duction in intensity of any part of the spectrum when the chemical action 
is reduced. Professor Crew estimates from 5 to 100 times as the reduc- 
tion in intensity caused by the hydrogen atmosphere. The electrical 
cause alone can account, then, for only a small part of the radiation. 
The secondary causes play very important parts. 

If all the lines of the spectrum of this arc were the same function of 
the causes of radiation, then all the lines of the spectrum would be 
uniformly reduced in intensity upon the reduction of chemical action. 
Experiment shows this hypothesis to be too broad, but the lines belong- 
ing to the series of Kayser and Runge are uniformly reduced in intensity, 
so that it is probable that these lines are all the same function of the 
causes of radiation. 


Of the other lines, those which are reduced more in intensity than the 
series lines, must be less intimately related to the electrical or thermal 
causes of radiation than are the series lines. 

Let us agree that the average intensity of the spectrum of the arc in 
hydrogen is only one fifth of its intensity in air, and let us agree that 
the electrical cause of radiation remains practically constant with constant 
current and voltage although the general intensity of the arc is greatly 
reduced by the hydrogen atmosphere, then it follows that of the total 
radiation, that fraction which must be attributed to the electrical cause 
alone, is relatively five times as great in hydrogen as it is in air. Any 
line, therefore, which is a function of the electrical cause alone, should 
have in hydrogen five times the relative intensity that it has in air. It 
seems quite likely that this may account for the appearance in hydrogen 
of numerous strong spark lines, not found in the arc in air. 

The appearance of the spark lines in hydrogen is not confined to the 
rotating arc; the magnesium spark line at 4481 appears clearly in the 
stationary metallic arc in hydrogen but not in air. The above explana- 
tion for the appearance of these lines makes it probable that the electri- 
cal cause of radiation is not zero in either atmosphere. 

In the rotating arc the current is interrupted about twenty-five times 
per second when the rotating electrode is a rod, instead of a disc, of 
metal, and this spark at the breaking of the current may account, in part, 
for the appearance of these spark lines in hydrogen. But we may in- 
quire why this spark should partake any more of the nature of the true 
spark in hydrogen than in air. The reduction of the chemical action in 
the arc reduces the temperature and conductivity of the gases between the 
poles in hydrogen, and it occurred to me that this action may affect the 
appearance of the spark lines in either of two ways : — 

1 . It may be that a gas which is in the hot condition of the arc in 
air cannot give off spark lines; the arc spectrum may be characteristic 
of this condition of the gas and may have nothing to do with electrical 
action, and so, in this state, would give off only arc lines if a spark were 
passed through it. 

2. It may be that the conductivity of the gases in air is reduced so 
slowly at the breaking of the current in the rotating arc that the voltage 
of break never rises high enough to make a true spark. 

In either of these cases, in hydrogen, the hot gases are largely absent, 
owing to reduction of chemical action, and give opportunity for the spark 
to appear. 

In order to test the first suggestion I arranged an electrical circuit as 



shown in the diagram. The dynamo furnishes a direct current of 110 
volts, and when the switch was closed the current simply passed through 
the arc and the resistance in series. The arc was stationary, one 
electrode was carbon and the other a zinc rod. The induction coil used 
is a duplicate of the one designed by Professor Rowland to give a short 



Figure 1. 

spark but a very powerful discharge ; an alternating current of 110 volts, 
6 amperes, was run through the primary, without an interrupter. The 
condenser used has a capacity of fa microfarad. It will be noticed that 
the spark can take place only by passing in succession the two gaps 
marked "arc" and "spark." The spectroscope is adjusted to observe 
phenomena at "arc" gap. 

In performing this experiment I first turned on the spark and set the 
cross-hairs of the eyepiece of the 10-ft. concave grating upon the zinc 
spark line at 5895, between the D lines of sodium. The spark was 
turned off and the arc turned on. The spark lines no longer appeared, but 
came out instantly when the spark was again started along with the arc ; 
both arc and spark were now running through the gap marked " arc " 
and the spectroscope showed both arc and spark lines. Now while both 
currents were on, the arc current was turned off ; the arc spectrum dis- 
appeared, but the spark spectrum persisted with apparently the same 
intensity as before and without an interval of darkness. 

This experiment shows that the first suggestion is not true ; that the 
arc spectrum is not characteristic of the condition of the gases in the arc, 
and makes it highly probable that the electrical cause of radiation is 
not zero. 

In order to test my second suggestion above, I short-circuited the 
spark gap shown in Figure 1. The spark line appeared as before in the 
spark, but disappeared as soon as the arc current was made ; the arc and 
the spark discharges were both passing through the arc as before ; I had 


simply cut out the " spark " gap, but the spark line could not be seen 
when both currents were on. Now when both currents were on I broke 
the arc circuit, and nothing at all could be seen in the spectroscope ; 
neither the arc nor the spark lines remained, although the spark current 
was still passing. After remaining at the eyepiece of the spectroscope 
about one second I began to see traces of the spark lines, and then they 
soon came out with their usual brightness, and the spark discharge which 
had been silent during that second of darkness assumed its usual noisy 

This experiment shows that the gases of the arc do not furnish enough 
resistance to the passage of a high voltage alternating current to cause 
the discharge to assume the character of a spark for a full second after 
the breaking of the arc current. This seems to confirm the second 
suggestion above, to the effect that the conductivity of the gases de- 
creases so slowly on the breaking of the arc current in air as to give rise 
to no very high voltage, and so accounts for the non-appearance of the 
spark lines in the rotating arc in air. 

These two experiments throw an interesting light upon the nature of 
the spark. The spark at the arc gap in these experiments seems to be 
due to neither the current nor to the voltage, but to some kind of an im- 
pulse furnished by the sudden rush of electricity across the auxiliary 
" spark " gap. 

In the second experiment, above described, the spark lines do not all 
seem to come out at the same time. I hope in the near future to be 
able to arrange an automatic apparatus for making and breaking the 
currents and an adjustable occul ting-screen which will enable one to 
photograph the spectrum of the spark at definite intervals of time after 
the arc current is broken. A series of these photographs will probably 
furnish an interesting story of the development of the spark spectrum. 

Physical Laboratory, 
Northwestern University. 


Plate I, Figure 1. Tin arc in hydrogen, 1st order. 

Plate I, Figure 2. Upper part, copper arc in hydrogen, 1st order. Lower part, 
copper arc in air. 

Plate I, Figure 3. Tin arc in hydrogen, 1st order. All lines are second order 
except H a at 6563. 

Plate I, Figure 4. Copper arc in hydrogen, 2d order, showing hydrogen-copper 
fluting and the H y line. 

Plate II, Fig ore 1. Aluminium arc in ammonia, 2d order, showing hydrogen- 
aluminium fluting. 

Plate II, Figure 2. Middle, magnesium arc in hydrogen, showing hydrogen- 
magnesium fluting at 5210, 1st order. Outside, magnesium arc in air. 

Plate II, Figure 3. Upper part, zinc arc in hydrogen, 1st order, showing hydro- 
gen-zinc lines. Lower part, zinc arc in air. 

Plate II, Figure 4. Sodium (and copper) arc in hydrogen, 1st order, showing 
hydrogen-sodium lines. 












<n . 
























O _ 






CD ' 











































to — « 

— _>_> 














Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 7. — August, 1901. 



By Theodore William Richards. 


By Theodore William Richards. 

Received July 27, 1901. 

The long continued discussion concerning the relative advantages of 
hydrogen and oxygen as standards of the numerical values of chemical 
combining weights seems to need yet another word. In spite of the 
fact that an international committee has decided by a large majority 
in favor of oxygen, the opposing arguments have not been put to rest. 

The latest paper on this subject is by Erdmauu,* the well known 
champion of the old unit value for hydrogen and the new value for 
every other atomic weight. The paper consists mainly of a partial 
reply to an earlier paper by Brauner.f The weight of the argument 
in these papers seems to be distinctly on Brauner's side, but it is not 
my purpose to recapitulate all the arguments which these gentlemen 
and others have advanced. | I wish rather to call attention to a few 
points wliich do not seem to have received the attention which they 

The first of these concerns the question of fact. What element has 
served as the actual standard of comparison in a plurality of cases? 
The question is easily answered by referring to Clarke's valuable 
compilation. § 

Evidently hydrogen in combination has been weighed accurately only 
in the cases of water and the ammonium salts. The atomic weights of 
zinc, aluminum, iron, nickel, cobalt, and gold have been determined by 

* Zeitschrift fur anorg. Chem., 27, 127 (1901 ). 

t Zeitschrift fur anorg. Cliem., 26, ISO (1901). 

J A recent recapitulation of many of the arguments on each side may bo 
found in the report of the American Chemical Society's branch of the International 
Committee, published in the Journal of the American Chemical Society, February, 
1901, p. 44 of the Proceedings. 

§ F. W. Clarke, A Recalc. of the At. Weights, Smithson. Misc. Coll., The Con- 
stants of Nature, Part V. (1807). 


measuring or weighing the hydrogen which they displace or to which 
they correspond, but the results of different experimenters are far from 
concordant. All other elements beside these eight have been referred 
to hydrogen only with the assistance of oxygen. 

On the other hand, oxygen has been used as the direct standard of 
reference in countless cases. The determination of oxygen in the chlo- 
rates, bromates, and iodates may be considered as the starting-point for 
the calculation of Ag, K, Na, CI, Br, and I, and through them of very 
many others. Into this remarkable series of experiments, executed in 
great measure by Stas, the value of hydrogen enters only in the case 
of amnionic salts. If the atomic weight of nitrogen were certain, we 
should indeed have here a direct basis of comparison, but unfortunately 
the value for this element may be as much as 0.05 per cent, or even 
more, in error. The direct practical determination of the exact com- 
position of ammonia gas, either by analysis or synthesis, has not yet 
been accomplished. The value for nitrogen depends largely upon the 
analysis or synthesis of nitrates, thus making oxygen the essential stand- 
ard of reference in this case also. The other elements which have 
been determined more or less accurately by reference to oxygen are as 
follows : H, C, Cu, Ca (through the carbonate), Pb (through the 
nitrate), Zn, Cd, Hg, Tl (through the nitrate), Sn, P, As, Sb, Bi, Mo, 
U, W, Se, Te, Mn, Fe, Ni, Co. If one adds to these all those which 
are connected less directly with oxygen through the halogen and silver 
values and the sulphates, all the chemical elements are included in the 
list. Thus an overwhelming majority of elements is referred more 
directly to oxygen than to hydrogen. 

Erdmann points out in his recent paper that there are possible causes 
of error in some of the methods used by Stas for the analysis of chlo- 
rates. Unfortunately he does not touch upon the very important ques- 
tion of the percentage effect of these causes of error. It is undoubtedly 
true that in these cases, as well as iu every other case, absolute accuracy 
was not attained. No analytical method is wholly free from the possi- 
bility of error, and hence it is vain to expect that any table of atomic 
weights should be perfectlv trustworthy. When the accuracy of Stas 
has been exceeded in actual fact, it will be time to forsake his results 
for the newer values. 

Erdmann su<rgrests that silver be chosen as the standard of reference, 
and the suggestion is one which has some advantages. On the other 
hand the tendency which this metal has to absorb oxygen has cast a sus- 
picion over some of the work in which it was used. A further objection 


to silver lies in the fact that it cannot be directly used in the demonstra- 
tion of Avogadro's rule. Moreover, one is in doubt as to the value to 
assign to this element, supposing that it should be selected as the stand- 
ard. According to Erdmann's earlier arguments, logically followed out, 
one should make silver 100.000, but this would cause hydrogen to be less 
than unity. If silver is taken as 107.11, hydrogen would be 1.000 at 
the present time, but what it might be in the future no one can predict, 
since hydrogen is compared with silver at present only in a roundabout 
fashion. Hence each of these assumptions would bring with it a further 
disadvantage besides that attending the immediate inconvenience of using 
new values. 

The most important argument used by the minority is the pedagogic 
one. It is contended that the uneven value for hydrogen, 1.0075, com- 
plicates the explanation of the very important rule of Avogadro. If 
this were true, it would indeed be worthy of consideration, but according 
to my experience there is no difficulty in the matter. 

For some time I have abandoned the comparison of specific gravities 

as a means of demonstrating Avogadro's rule. I have used instead the 

densities of gases and vapors, — that is, the actual weights of a litre of 

the several substances at 0°C, or at 273° C or at 546°C. This seems 

to be a more successful method, probably because density has concrete 

dimensions, and is not a numerical abstraction as specific gravity is. 

1.97 x 
The student at once comprehends the equation of ratios -^— - = • 

If the exact experimental values for the densities of the two gases arc* 
given, the solution of this equation gives the student not only the ob- 
served molecular weight of carbon dioxide, but also an insight into the 
extent of the actual deviations from Avogadro's rule. Since the intro- 
duction of this method of presentation, I have had far less trouble, and 
far more successful examination results, than were formerly obtained. 
The student usually learned by heart the old rule, "The molecular 
weight equals twice the specific gravity," without understanding it. 
Because the density-method would serve equally well with any gas 
used as a standard, the pedagogic argument against II = 1.0075 seems 
to me illusory. 

The argument just discussed has led the Committee of the German 
Chemical Society to an action which seems to me exceedingly unfortu- 
nate, — namely, the publication of two tables of atomic weights. This 
action has already been criticised by Krister and others. Either table 
alone, supported by suitable weight of opinion, would have been vastly 


better than two. The mistake is especially to be regretted because the 
eminent committee in question has previously acted with so' much wisdom 
and ability. 

It seems to me that by far the most important questions which have 
been raised in the whole discussion are the questions of uniformity and 
permanence of usage. These were indeed the prime objects of the foun- 
dation of the German Committee in the first place. Nothing could be 
more destructive to accurate calculation than a changeable standard of 
measurement ; and yet this very uncertainty marks the present state of 

I cannot but think that every one should accept the standard of refer- 
ence upon which any considerable majority of representative chemists 
agree, since the matter is rather a question of convenience than a ques- 
tion of principle. In the first place I preferred O = 16.000 primarily 
because so much valuable work, both in analytical and in physical chem- 
istry, has already been calculated upon this basis, and because of the 
effect of a possible change in the oxygen-hydrogen ratio. At pres- 
ent a still more important reason for preferring this standard exists, 
namely the action of the International Committee, consisting of some of 
the most prominent chemists of many countries, appointed for the ex- 
press purpose of voting upon this question. This Committee, by a large 
majority, decided to call oxygen exactly 16.000. I cannot avoid the 
belief that until a yet more representative body of chemists is appointed 
by international co-operation, or until the present committee reconsiders 
its vote in parliamentary fashion, the present verdict of this committee 
should rule the chemical world. Unless chemists are prepared to ac- 
cept such a ruling, the appointment of an international committee is a 
waste of time. 

Representative government in civil affairs would be impossible if the 
minority refused to act in accordance with the decision of the majority. 
Does not the same principle apply to scientific rulings ? Of course 
intelligent discussion is always desirable — the restriction applies to 
action and not to speech. Before the action of the International Com- 
mittee the situation might have been called one of scientific barbarism. 
but at present it may be called one of scientific rebellion. 

Formerly new determinations of atomic weights made at Harvard 
were expressed in publication both upon the basis O = 16.000 and 
upon the basis O = 15.879, because the question had not been decided 
by representative vote. In future, out of respect to the action of the 
International Committee, only the former standard will be used iu this 


Laboratory. If an adequate internationally representative body of 
chemists should in the future decide that some other standard is better, 
immediate change of practise will be made to suit the new decision. 
One regrets that so much time should have been spent in discussing a 
matter which involves no fundamental principle, but is simply a question 
of form and of convenience. 

The subject matter of the present paper may be summed up in the 
following sentences. It is pointed out that oxygen has actually served 
as the experimental standard of reference in a great majority of cases, 
that a great bulk of valuable work has already been published on the 
basis O = 16.000, and that the use of this standard involves no impor- 
tant didactic difficulties. It is further contended that the decision of 
the representative International Committee is in itself an important rea- 
son for adopting this standard, and that uniformity of usage is more 
important than any of the special advantages claimed by either side in 
the discussion. 

Seal Haruor, Mt. Desert, Maine, 
July 22, 1901. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 8.— October, 1901. 


E. L. MARK, DIRECTOR. — No. 127. 


By Peter Frandsen. 

E. L. MARK, DIRECTOR. — No. 127. 


By Peter Frandsen. 

Presented by E. L. Mark. Received September 3, 1901. 


Introduction .... 
Tliigmotaxis .... 
Material and Methods 



Methods ... 
Operations and Results 



Summary of Part II . 

III. Pliototaxis 


Operations and Results 
Summary of Part III 
Bibliography . . . 



The following studies were made at Harvard University during the 
fall and winter of 1898-99. The problem was proposed by Dr. C. B. 
Davenport and the investigation carried on under his immediate direc- 
tion. I wish here to acknowledge my indebtedness to his many sugges- 
tions and helpful criticisms throughout the year. In connection with the 
preparation of the manuscript for publication, I am under obligation to 
Dr. E. L. Mark for many kindnesses. 

The behavior of any organism toward artificial stimulation is prob- 
ably always largely dependent on its normal environmental condi- 
tions. The long action of those conditions, assisted, perhaps, by the 
animal's own efforts, conscious or unconscious, to adapt itself to them, 
finally results in certain habits and instincts. The process of adaptation 
being extremely slow, organisms are strongly averse to great or sudden 
changes in their environment and incapable of adjusting themselves to 
them. As a rule, then, we should expect animals to seek those condi- 
tions of light, heat, moisture, and other physical and chemical influences 
which are most in accordance with those to which they are normally 


The most easily observed responses of animals are naturally those 
which find their expression in locomotion. The number of stimuli which 
may influence locomotion are, of course, numerous, but of these a certain 
limited number play much the larger part. If we had an accurate 
knowledge of the relative weight of these different forces, we might pre- 
dict with certainty the path any animal would follow under certain given 
conditions. An experimental study of the different stimuli ought at least 
to enable us to find out which ones do operate, and perhaps to establish 
certain general laws regarding them and the biological tendencies which 
impel the animal to respond. 

The present paper is a study of the locomotor responses of the slug 
Limax maximus to three kinds of stimuli, — those of touch, gravity, and 
light. In connection with these studies new problems have constantly 
arisen, some of which have been cursorily considered, many others 
merely alluded to, so that the work is far from being complete. 

The term " geotaxis " has been used to designate the influence of gravity 
on locomotion. Interesting and careful studies have been made on the 
geotaxis of numerous Protista by Schwarz ('84), Aderhold ('88), 
Massart ('91), and Jensen ('93). These investigations clearly show a 
geotactic response in the unicellular organisms studied. The kind of 
response varies according to other conditions, such as those of light, heat, 
density of medium, chemical influences, etc., and may also differ in indi- 
viduals of the same genus under apparently like conditions. Massart 
('91, pp. 161-162) found that, when a number of Spirilla were put into 
a vertical tube, one group collected in the upper part and another at the 
lower part. He also found (p. 164) that Chromulina woroniniana was 
negatively geotactic — that is, moved upward, or in a direction opposite to 
that of the pull of gravity — at 15° to 20° C, but positively geotactic at 
5° to 7° C. Jensen's work also showed the important influence of other 
agents in modifying geotaxis. Loeb ('88, pp. 7-8) found that cock- 
roaches preferred the steepest side of a box whose four sides were inclined 
at different angles ; that is, they are negatively geotactic. He also dis- 
covered that a number of other Metazoa were geotactic. 

In a certain way, the present paper is a continuation of a recent study 
made by Dr. C. B. Davenport and Miss Helen Perkins on geotaxis in 
the slug. Davenport and Perkins ('97, p. 105) discovered that the 
intensity of the animal's geotactic response was directly proportional to 
the sine of the angle of deviation from the vertical, and hence " varied 
directly as the active component of gravity." In the third section of 
their paper, the question, " What determines whether the head end of 


the slug shall be directed up or down ? " was raised and considered. The 
results showed that certain individuals appeared to have a fairly marked 
positive geotaxis, for, when placed on an inclined glass plate, such 
animals swung the head-pole of the axis toward the earth ; but others 
showed as strongly marked a tendency to move away from the earth, and 
a few seemed indifferent as to whether they went up or down. Their 
experiments showed further that there was, apparently, no inherent 
tendency in individual animals to move either to the right or to the left, 
so that the difference in geotactic response could not be explained as due 
to differences of an inherent tendency of this kind. The effect of a slight 
initial impulse given to the head of the animal indicated that the thigcno- 
tactic, or contact, stimulus imparted to the animal in handling might, to 
some extent, modify its response to the stimulus of gravity. But 
Davenport and Perkins did not reach any definite, satisfactory answer to 
the main question. 

It was to test their observations by a larger number of experiments, 
and, if confirmed, to explain them by further experimentation, that the 
present investigation was undertaken. In the first place, I wished to 
find out whether certain individuals, if put on an inclined glass plate, 
always responded to the pull of gravity by directing the head end up and 
moving away from the earth, and whether certain other individuals 
always did the contrary. If this proved to be true, then it was my main 
problem to seek the reason for it. Is the force which makes some slugs 
go up, others down, and still others indifferent to the attraction of gravity, 
a purely accidental one, — is it a physical force, or is it what we may call 
a psychical peculiarity, which varies in different individuals and in the same 
individual at different times ? As a preliminary to the main problem, 
I first made a series of experiments on the animal's thigmotaxis, — its 
response to contact- and pressure-stimuli. By virtue of its thigmotaxis, an 
animal moves either toward or away from the agent which comes in 
contact with it, just as its geotaxis is expressed in a movement toward or 
away from the earth, in response to the attraction of gravity. 

I. Thigmotaxis. 

Material and Methods. — The animal used in all the following experi- 
ments was Limax maximus, which is fairly abundant in the greenhouses 
about Cambridge. Material was obtained from several different green- 
houses and kept in a large closed tin box, the bottom of which was 
covered with moss kept moist, so as to afford an environment as much like 
the customary one as possible. Fresh cabbage leaves constituted the 



animal's main food. The cannibalistic tendencies of the slug, together 
with an unavoidable deterioration due to repeated handling, necessitated 
a frequent renewal of the animals. 

The methods used in the experiments were simple. The slug was 
placed on a circular glass plate set horizontally in the bottom of a 
cuboidal wooden box which was made impervious to light and covered 
with a thick, black cloth. Precautions were taken to avoid thermal and 
chemical influences by keeping the box at as equable a temperature as 
possible and by wiping the plate free from slime before each test. The 
tests were made only when the animal had definitely oriented itself and 
was moving ahead in a straight line. Two series were made. In the 
first series the dorsal tentacle was touched gently with the forefinger. 
The box was then immediately covered with the black cloth. Observa- 
tions were made after the lapse of 20 to 30 seconds and the position of 
the animal noted. The right and left tentacles were touched alternately. 

Results. — The following Table (I.) gives the results of a number of 
experiments on ten different animals. 

Response to Thigmotactic Stimulation of the Tentacles. 

Number of Trials. 



Total Number 
of Trials. 



















































Totals . . 






The column headed with the minus sign shows the number of times the 
animal responded by moving away from the source of stimulus; the one 
headed with the plus sign, the number of times it moved towards that 
source ; and the zero column, the number of times there was no response. 
I found that the animal would respond very definitely and precisely to 
stimuli two or three times in succession by immediately retracting the 
tentacle touched and moving away from the stimulating influence. After 
the third trial, however, it either refused to change its direction of loco- 
motion or else moved directly towards the source of the stimulus. If a 
respite of a few seconds before the next stimulation was then permitted, 
the animal would again give a precise negative response for two or three 
trials, and then, as before, it desisted. Out of the total 145 tests, there 
was a negative response in two thirds of the trials. The remaining 
trials — one third of the whole — were about equally divided between 
the positive responses and refusals to respond at all. Sometimes five or 
six tests were made in quick succession, so that the total negative 
response is rather less than it would have been if a rest had been given 
in each case after three tests. Out of the 21 cases of direct positive 
response, 15 were cases where the right tentacle was touched, and the 
remaining 6 were due to stimulation of the left tentacle. Similar, but 
more marked, differences between the results of stimulating the right and 
the left tentacles were observed in other experiments. This suggests that 
either the right tentacle may be less sensitive to stimuli, or that its coun- 
terirritancy may be more readily aroused. There is, however, a third 
possible cause. The animal may have an innate tendency to go to the 
right, and, if so, this tendency may diminish to some extent the force of 
the stimulating agent when it impinges on the right side of the animal, 
and correspondingly increase the response when the stimulus is directed 
upon the left side of the animal. Something further will be said about 
this point in a later part of the paper. 

A few thigmotactic experiments were next made on the sides of the 
animal posterior to the head. The right and left sides were touched 
alternately. The results are given in Table IT. 

Phenomena like those observed in stimulating the tentacles are seen 
here, and they also agree with similar observations by Davenport and 
Perkins ('97, p. 109.) After two or three trials, the animal begins to 
show resistance, and if the finger is held against its side, will sometimes 
try to displace the finger by pushing against and curling the body around 
it. The frequency of the negative response is here somewhat less marked 
than in the preceding experiments, which is as we should expect, owing 



to the greater sensitiveness of the tentacles as special tactile organs. In 
these experiments every one of the minus and zero results was due to 
stimulation of the right tentacle. 

Response to Thigmotactic Stimulation of the Sides of the Body. 



Number of Trials. 

Total Number 
of Trials. 













Totals . . 





These facts clearly prove that, under ordinary circumstances, the slug 
is negatively thigmotactic. In our consideration of the animal's responses 
to other stimuli, we shall have to take this into account, as causing 
occasional vagaries, and therefore endeavor to eliminate it as much as 
possible from the experiments. 

II. Geotaxis. 

What determines whether the head end of the slug shall be directed 
up or down ? 

Methods. — The same apparatus was used as in the preceding experi- 
ment. A circular glass plate was employed so that the animal could be 
rotated into any desired position without the necessity of its being 
handled. The plate was set in a box at an augle of about 45° with the 
horizon. In each test the animal was so placed on the plate that the 
long axis was horizontal, different sides being directed downward in 
different trials. At first the experimentation consisted mostly of watching 
the animals in order to obtain some clue for further work. Later, rough 
sketches of the pigment patterns of the individual animals were made, so 
that it was possible to identify individuals with certainty ; the same 
animal could then be subjected to experiments at different times and the 
difference in results noted. The methods used in working out particular 


questions will appear as these questions are considered. As the same 
number of experiments were not made on each animal studied, I have, 
for the sake of comparison, estimated in each case the geotaxis in per 
cents. This percentage is obtained by dividing the number of positive 
or negative responses by the total number of responses. The nearer the 
geotaxis percentage approaches 100 the more precise has been the kind 
of response. No fixed time was allowed to elapse between successive 
tests, but in'each test the observation was made at an interval of from 30 
to 60 seconds after covering the box. 

Operations and Results. — The first question investigated was whether 
particular animals exhibited a decisive positive or negative geotaxis. A 
number of tests were, therefore, made on each of several selected indi- 
viduals. The results obtained were like those of Davenport and Perkins 
('97, p. 108) ; that is, certain animals showed a very marked positive geo- 
taxis ; others, an equally decided negative tendency ; and a few, perhaps 
one animal out of 12 or 15 where' 10 or more tests were made, were 
apparently geotactically indifferent. The occasional irregularities in the 
responses of individual animals were easily seen to be due to influences 
other than pure gravity, such as jarrings of the plate, influence of contact 
in putting the animal on the plate, and to the influence of light admitted 
in lifting the cover of the box. Frequently, upon the raising of the 
cloth to make an observation, the animal would retract its tentacles, as 
if dazzled by the sudden inflow of light, and at the next observation 
it would be seen to have altered its response. 

Naturally, this question next arose, Is the response the same on 
different days? In Table IV. (p. 195) are given the results with a num- 
ber of animals experimented on to test this point. These are numbers 
2, 7, 8, 22-25, 27. Number 2 was positively geotactic on two days 
and negative on another day. A similar variation is seen in the case 
of slugs 7 and 22. In the case of all the rest, however, there is a very 
marked constancy. The ninth (last) column in the table indicates the 
condition of the animals at the time of experimentation. We see from 
this that on the days of different response, the animals were in somewhat 
unlike conditions, which may account for the irregularity of response. 
The significance of this will be dealt with later. The important matter 
here is, that the animals, when in the same condition and under the 
same circumstances, have a fairly constant geotaxis from day to day. 
One of the most marked cases is that of number 24. This animal was 
experimented on at different times for a period of three weeks. During 
this period, it was always active and in good condition, and, as the 



table shows, at all times, exhibited nearly the same percentage nega- 
tive geotaxis. At the last trial made, it responded irregularly, and so 
slowly, — at one time not changing its position for thirty minutes, — 
that I had to give up the attempt to obtain a series. This was often 
the case with other individuals after a few definite responses. 

Tests were then made on the geotaxis of the same individuals at 
different times of the same day. Considering the slug's normal en- 
vironment, it would not be surprising if, for instance, it should show an 
upward tendency in the evening and a downward geotaxis in the day- 
time. Its nocturnal habits and dislike of daylight might give it a dif- 
ferent geotactic instinct at night from that of the daytime. I insert here 
a table (III.) giving the results of a few experiments bearing on this 
point. As the table shows, the response is pretty constant at different 

Geotaxis of three Individuals at Different Times in the Day. 

Number of Trials. 



Time of Day. 

% Geotaxis. 

of Mucus. 




8.00 A.M. 





1.30 p.m. 




Rather Dry 

8.30 p.m. 




Tail Dry 


1.30 p.m. 





7.00 p.m. 




Rather Dry 

7.00 p.m. 





10.00 p.m. 






7.00 A.M. 





1.30 p.m. 




times of the same day. The one exception is number 2. That it 
was negative on one evening at 7 p. m., may be explained by the fact 
that its condition was not good. Moreover, on another evening at the 
same time the animal had become positively geotactic. 

From the observations recorded in Tables III. and IV., it is plain that 
the geotactic response is not due to purely accidental factors, but can 


be explained only by some marked difference between the individual 
animals. The first thought is that differences in response are due to a 
difference in size, and the facts seem to give some support to that ex- 
planation. Most of the positively geotactic individuals were found 
among the small and medium-sized animals, and nearly all the negative 
animals were of large size. Moreover, the few indifferent individuals 
were of medium size. This, however, was not an invariable rule. 
Small animals were sometimes negatively geotactic and, occasionally, a 
large slug would migrate earthward. 

A second, clearly important, factor is the condition of the animal's 
mucus. As shown by the preceding experiments, animals, positively 
geotactic when normal, became negatively geotactic when lacking in 
an abundance of sticky slime ; e. g. animal 2, Table III., and animals 2 
and 7, Table IV. On the other hand, in one instance (22 b), a nega- 
tive animal, when extremely sticky, went downwards. Abundant, sticky 
mucus is evidently connected with a downward migration, and dryness 
seems to force the animal to take an upward direction. But these facts 
are not enough to explain all responses. For sometimes two animals 
of nearly the same size and in equally good condition gave different 
geotactic responses. We must look for other differences. It will, 
however, be necessary first to refer briefly to the form and external 
appearance of the slug. t 

mtlp. ofpul. m( i a // l ¥ 


Figure 1. 

Outline of Limax maximus. mtl. a., anterior edge of mantle ; mtl. p., posterior 
edge of mantle ; a. to mtl. />., anterior region of body ; mtl. p. to p., posterior region ; 
oc, eye ; ta. d., dorsal tentacle ; ta. v., ventral tentacle ; of. pul., pulmonary orifice. 

The slug, if we except the respiratory opening on the right side of 
the body, is externally bilaterally symmetrical. It has no external 
shell. There are two pairs of tentacles, — a dorsal pair bearing the 
eyes and a smaller ventral pair. The mantle extends from the neck, 
ventrally, to near the edge of the foot. Posteriorly, it forms a prominent 
fold, as indicated in the figure, which may be used to separate the body 
into an anterior and a posterior region. Observations of the animal 
vol. xxxvii. — 13 


reveal that it has very different degrees of control over these two 
regions of the body. In locomotion, the head end of the body, back 
as far as the respiratory opening, is freely swung about from side to 
side and determines the axis of orientation of the animal. Over the 
posterior region, the animal seems ordinarily to have very imperfect 
control. The relation between the two regions is crudely that of a 
span of horses to a chain of wagons which they are pulling. When the 
horses change direction, the wagons come only slowly around into posi- 
tion one after the other, and there is likely to be some slipping in the 
process, especially if it takes place on a down grade. In watching the 
slug, I saw that the adhesion of the anterior region appeared consider- 
ably greater than that of the posterior. When the animal gets dry, it 
does so first at the posterior region. The tip of the tail is the part first 
to lose its clinging power, and it may curl up dorsally as a result of the 
drying process. If an animal which is thus beginning to deteriorate in 
its supply of mucus be put on a glass plate and the plate raised into a 
vertical position, the slug will move along and desperately cling to the 
plate with the anterior part of its body. The posterior region will 
gradually swing downward as a result of the pull of gravity, and, in 
consequence, the animal's head will eventually be directed upward. 
From this, we are justified in concluding that the same principle will 
operate, although to a considerably, less degree, in the animal's normal 
condition. A hasty examination showed that there was a good deal of 
variation in the proportions of the two regions in different individuals. 
As a crude and easy way of estimating these proportions, I measured 
the length in millimeters of the anterior region from the tip of the head 
to the posterior fold of the mantle, and similarly the length of the pos- 
terior region from that fold to the tip of the tail.* 

The results from 27 animals thus measured are given in Table IV. 

The individuals (Table IV.) are arranged in a series, beginning with 
those in which the two regions are most nearly of the same length 
and ending with those in which the disproportion is greatest. In animal 
No. 1, the length of the anterior region is 83.3 per cent (column 8) of 
the posterior ; that is, the ratio is almost one to one. In No. 25, the 
anterior region is only 45 per cent as long as the posterior, or less than 
half its length. 

The fifth column in the table gives the geotaxis of individuals in per 

* The measurements were made when the animal was extended and moving 
across the plate. The amount of elongation varies a good deal, but the regions 
retain pretty closely their relative proportions. 






Animal se 

No. oi 


•iesof ( 

)b- Number of Trials, 


Length of 


Region in 


Length of 


Region in 


Ratio of Ant. 
to Post. Re- 
gion in per 

Condition of Animal. 

) Diffe 
it Days 

r- " 















4- 0(5.0 









- 72.2 









+ 70.5 















+ 85.7 









+ 71.4 







+ 87.5 

















+ 60. 




Rather dry. 





+ 70. 












Tail slips. 





+ 66.6 









+ 94.4 











Tail slips. 




- 80. 




Mucus watery. 





+ 82.3 
















- 70.5 







• > 


- 72.7 








+ 75. 








- 88.8 















- 70. 








+ 72.7 




Extrem'ly sticky. 










' 5 









- 75. 









- 53.3 









+ 61.5 




Very sticky. 





- 64.2 









- 62.5 

























- 83.3 









- 82.3 









- 90.5 









- 82.6 









- 82.3 









- 70.8 









- 77.7 















15 ■ 

- 83.3 

















- 83.3 






cents. The table includes those animals which were fairly active in 
response but does not give individuals obviously unable to respond 
because of a lack of slime secretion. The positively geo tactic animals, 
with two exceptions, are all found in the upper half of the table and 
almost all the negative animals in the lower half. Supposing other 
conditions the same, we can say that those animals in which the ratio 
of anterior to posterior regions is as 2 : 3, or greater, will be positively 
geotactic. Those between the ratios of 2 : 3 and 3 : 5 will be more 
uncertain in their geotaxis, which will depend largely on the combina- 
tion of other conditions. Finally, those in which the ratio is less than 
3 : 5 will almost invariably be negatively geotactic. The nearer one 
gets to the extremes, the greater the accuracy of prediction. This pre- 
diction, it is understood, applies only to animals tested on the glass plate. 

An examination of the ninth column shows that the few cases of nega- 
tive geotaxis occurring in the positive half of the table are probably due 
to a deficiency in the second most important factor affecting the geotaxis ; 
namely, the condition of the slime secretion of the animal. This 
secretion may be deficient either (1) in quantity, as in the case of slug 
2 b ; or (2) in quality, as was the case with slug 10. Of the two cases 
of positive geotaxis occurring in the negative half of the table, the first, 
that of slug 18, is easily explained as due to an extraordinary tenacity 
of the mucus. Moreover in this, and more markedly in the case of 
slug 22 b, the slugs were very large and rather slow in their movements. 
Slug 22 b, instead of moving ahead actively, like most slugs when in 
good condition, often swung its head toward the earth without any fore- 
ward movement, and hence did not give the pull of gravity the most 
favorable opportunity to work on the posterior region of its body. This 
connects itself with a general observation on all the animals. When 
active, they are usually very precise and uniform in their responses. 
If stupid, slow, and averse to movement, — a condition in which the 
best of them sometimes get, — they will either obstinately refuse to 
move, or else, keeping the posterior region firmly fixed, will swing the 
head end toward the earth. Sometimes such a slug will slowly move 
in a circle, first down then up, and finally curl itself up, like a dog by 
the fireplace, and apparently go to sleep. This peculiarity may be 
connected with the food conditions of the animals, as will be shown in 
a set of experiments to be given later on. 

The two most important factors in determining the geotaxis of indi- 
vidual slugs are, therefore : first, the proportion of the anterior (mantle- 
covered) and posterior (uncovered) regions of the body ; secondly, the 


character of the slime secretion of the animal. If accurate measure- 
ments were made of the two regions of the body, we might obtain ex- 
actly the relative weights of these two factors. By means of a spring 
balance, the effectiveness of the mucus in counteracting gravity could be 
ascertained with a fair degree of accuracy. A large number of such 
observations in connection with geotactic tests might, finally, enable us 
to state precisely what combination of the two factors — weight of 
regions and strength of mucus — would be necessary to make an 
animal positively or negatively geotactic. I have made no such calcu- 
lations, and it would perhaps not be worth the trouble. The suggestion 
is instructive, however, as indicating the possibilities of predicting, with 
a certain degree of exactness, a phenomenon which seems at first sight 
to be entirely haphazard. Perhaps perfect mathematical exactness 
would, however, never be possible in this case, for, as I shall show a 
little later, other factors of importance probably enter in to modify 
the results. However, these too are not out of the reach of precise 

Certain slugs are negatively geotactic because gravity pulls the pos- 
terior region of the body down faster than it does the anterior region. 
Since in all slugs the posterior region somewhat exceeds in length the 
anterior, we should expect all animals to respond in the same way, pro- 
vided gravity acted in only a mechanical way. But about the same 
number of slugs go down as go up. Therefore, there must be some 
other factor, such as an inherent tendency, impelling these positive 
slugs to seek the earth. But if so, is it not probable that all slugs 
have this inherent tendency to move towards the earth, the tendency 
being obscured in the negative slug by the superior force of the me- 
chanical difficulties to be overcome ? The fact that positive slugs, 
when deficient iu means of resisting the pull of gravity, — that is, when 
dry, — assume a negative geotaxis, shows that the inherent tendency is 
sometimes obscured. If this hypothesis is true, then we ought to be 
able, by diminishing the force of gravity, or better, by increasing the 
animal's powers of resisting the disproportionate pull on the posterior 
region, to make the negative animals become positive. Similarly, if 
this mechanical difficulty of adhesion is the cause of negative geotaxis, 
we ought, by increasing it, to be able to compel positive animals to be- 
come negative. The first end may be attained by substituting for the 
glass plate a wooden one, which will presumably offer the animal a 
better chance of adhesion. The second end may be reached by substi- 
tuting for the glass plate one which has been coated with vaseline or 



a similar substance. Both ends may also be attained, to a certain extent, 
by increasing or decreasing the angle of inclination of the plate. An 
examination of the tables given by Davenport and Perkins ('97, p. 103) 
shows that the largest average number of negative responses occurred 
when the glass plate was vertical ; that is, when the mechanical diffi- 
culties were greatest. There is a gradual decrease in this average 
(and a corresponding increase in the average number of positive re- 
sponses), as the angles of inclination of the plate with the horizon were 
diminished from 90° to 60°, 45°, and 80° successively. At the still 
smaller inclinations of 22^°, 15°, 7°, and 0° (i.e., horizontal), however, 
there is on the whole an increase in the average number of negative 
responses, though this is quite irregular. Since the proportion of anterior 
to posterior region of the animals experimented on is not known, we 
cannot tell how far this factor may have been the cause of this irregu- 
larity in the sense of the response. 

I have made a few experiments by varying for the same individual the 
angle of inclination of the plate. The animals were all in good condi- 
tion throughout the experiments. The results — given in Table V. — 
show a decided increase in negative geotaxis with increase in the angle 
of inclination. 


Per Cent of Geotaxis at Different Angles of Inclination of the 


Number of Trials. 


Angle of 

% Geotaxis. 

of Animal. 






+ 80. 











+ 87.5 






+ 72.7 






- 80. 







The most striking case is the complete reversal of geotaxis, seen in the 
first animal experimented on. 



Still more conclusive results were obtained by the substitution of wood 
or vaselined glass surfaces for the clean glass plate. In order to make 
sure that the animal's power to hold on varied with different surfaces, 
and to determine approximately the relative strength of the adhesion, Dr. 
Davenport suggested the use of a delicate spring balance, such as are used 
in weighing letters. The animal was placed on a horizontal glass plate. 
When it had oriented itself, and was moving forward, the pan of a letter 
balance was held against the side of the animal and gradually increased 
pressure exerted until the animal was made to slip along the plate. The 
maximum reading (in ounces) on the indicator was noted. Then the same 
animal was placed on a wooden plate and a similar test made under 
like conditions of movement and activity. The same was done on the 
vaselined plate. A number of such tests were made on each individual. 
In order to avoid possible differences in results due to a gradual de- 
terioration in the condition of the animal, the sequence of the surfaces 
was varied in the successive sets (three) of trials so that each surface was 
once employed for the first experiment of a set. This method proved 
fairly satisfactory and gave in some instances very striking results. 


Amount of Tricssure required to dislodge the Slug from Different 

Horizontal Surfaces. 

Animal No. 



Vaselined Glass. 


1.8 ounces 

1.5 ounces 

.23 ounces 


1.25 ounces 

.67 ounces 

.34 ounces 


3.16 ounces 

2.16 ounces 

1.55 ounces 


4.33 ounces 

2.55 ounces 

1.55 ounces 


3. ounces 

1.16 ounces 

.50 ounces 


5.7 ounces 

3 50 ounces 

1.52 ounces 

The results recorded for each individual are the averages of three 
trials on each of the surfaces used. The table shows a considerable differ- 
ence in the degree of adhesion to the different surfaces. In the last four 
cases the animals were all very large. They were in excellent condition, 
having just been captured, and secreted a sticky slime in large quantities. 



After being ou the vaselined surface, there was a noticeable decrease in 
the power to hold on to the glass or wood, due probably to the vaseline 
which still adhered to the animal. Regarding these cases as typical of all 
slugs, we can say that the wooden surface affords a condition nearly 
twice as favorable as that of the glass plate for the exhibition of an inter- 
nal tendency. The vaselined surface, on the contrary, is only about half 
as favorable as the glass plate ; that is, it doubles the obstacles. As a 
general rule, owing to the irregularities of other influences, the differ- 
ence between the different surfaces would be, probably, somewhat less. 
For active, well-conditioned animals, however, we have no hesitation 
in concluding that the ratios obtained from these cases are fairly 

Having thus established the fact that the character of the surface does 
modify the animal's power to attach itself, I next give a table (VII.) 
showing the results of a series of experiments on twelve different individ- 

Geotaxis of the Slug on Different Surfaces. 


Ratio of 

Anterior to 


Parts in %. 

Plate at Inclination of 45 D . 

Wooden Plate. 

Glass Plate. 

Vaselined Glass Plate. 

No. of Trials. 



No. of Trials. 

n % ■ 

No. of Trials. 












+ 53. 











+ 54.5 









- 75. 









- 88.8 






+ 71.4 



+ 83.3 



- 75. 





+ 70. 



- 80. 






+ 90. 



- 90. 










- 60. 





+ 90. 







+ 83.3 



+ 83.3 



- 83.3 








— oo.o 








+ 77.7 




uals. The geotaxis of each animal was tested on three different sur- 
faces, — the glass plate, a circular wooden plate, and a glass plate coated 
with vaseline. Care was taken to have other conditions as nearly as possi- 
ble the same. Circular plates were employed so that the animal could be 
rotated into a horizontal position without being touched by the hand. In 
several cases a series was made on an animal using the glass surface ; 
the animal was then transferred to a wooden plate and the same number 
of trials made ; the same individual was then put back on the glass plate 
and as many more tests were made ; finally, it was returned to the wooden 
plate and an equal number of observations made. The same thing was 
tried alternating between glass and vaselined surfaces. 

The second column shows what per cent of the length of the posterior 
region of the animal's body its anterior region is, as previously defined. 
A comparison of the columns " % Geotaxis" under the different con- 
ditions at once shows, in nearly every case, a marked difference in the 
geotactic response with the three kinds of surfaces. The same number 
of trials was not always made on a given animal under the different con- 
ditions, so that the comparisons are not always on exactly the same basis. 
The results, however, prove pretty conclusively that all animals have an 
inherent tendency to move toward the earth. On the glass plate, the 
animals moving upward and downward are about equal in number, the 
rea-ons for which we have already given. On the wooden plate, which 
affords the best of the three surfaces for adhesion, all the animals have 
become positive. A vaselined surface offers still greater difficulties to 
positively geotactic responses; it compels the positively geotactic animals 
to become negative (Nos. 2,5, 8, 10). Some animals are utterly unable 
to adjust themselves to this extraordinary condition, especially if not en- 
dowed with the power of secreting excellent mucus. These animals either 
vainly cling with the anterior end of the body to the plate, while the poste- 
rior region slips downward, thus directing the animal up, or they roll off the 
plate altogether as soon as it is placed in an inclined position. For this 
reason some of the animals negatively geotactic on the glass plate gave 
no geotactic response when they were placed on the vaselined surface. 
These facts, then, conclusively answer in the affirmative our second ques- 
tion. All slugs have a tendency to move toward the earth. 

Now the question naturally comes up, Can we not assist this tendency 
in those animals which are negatively geotactic on a glass surface by 
bringing some other stimulus — light, for example — to bear upon them ? 
This slug is negatively phototactic to strong light, as the third part of 
this investigation will show. By exposing the animals to strong light, can 



we not make the desire for darkness cooperate with the inherent positive 
geotactic tendency to such an extent that the two together will over- 
come all mechanical difficulties and cause the animal to move downward ? 
The following table (VIII.) answers this question in the affirmative. 


Geotaxis of Slug on Glass Plate at an Angle of 45° influenced (1) by 
Gravity alone, and (2) by Gravity and Strong Light. 



Gravity alone. 

Gravity -f- Influence of Strong Light. 

No. of Trials. 

% Geotaxis. 

No. of Trials. 

»j Geotaxis. 












- 87.5 

— 75. 



+ 50. 
+ 58.3 
± 50. 
+ 66 6 
± 50. 

These experiments were carried on in the evening. The animal was 
first tested on a glass plate at an angle of 45° in the dark, in the ordinary 
way. Then it was placed on a horizontal glass plate and strong lamp 
light thrown directly upon it for a few seconds. In most cases it imme- 
diately gave a negative response to the light. When definitely oriented, 
the plate was again placed in the box at an angle of 45° and the box* 
covered with a black cloth. Two or three geotactic observations were 
then taken, and the animal again exposed to strong light. The expo- 
sure to light was repeated about three times in the course of ten observa- 
tions. The table shows that the influence of light has been to change a 
condition of strong negative geotaxis to one of indifference. The only 
exception is No. 6, which seemed little affected by the light. I hope to 
make a fuller study of the combined action of light and gravity later. 

It has been said that all slugs have an innate tendency to move toward 
the earth. Now, this tendency is probably due to the environment and 
habits of the animal. The slug, we know, is nocturnal in its habits. In 
the nighttime, it is actively moving about in search of food. In the day- 
time, it is inactive and seeks concealment, which is of course accom- 


plished by moving toward the earth. In hunting for food, it must 
naturally do some climbing. These facts lead us to expect a possible 
difference between the geotactic response of the nighttime and that of 
the daytime. My experiments in this matter, however, gave inconclusive 
results. But the animals experimented on were not in their normal en- 
vironment. There was no light and little change in temperature to assist 
the instinct, if it exists, in divining night from day. Moreover they did 
not have to seek food, for it was constantly supplied them. Such being 
the case, the instinct of concealment would be the main environmental 
influence on the animal, and this impels it toward the earth. 

These experiments have shown, then, that when the mechanical con- 
ditions are favorable, most animals exhibit a positive geotaxis. This is 
as we should expect. There were, however, a few exceptions. A few 
animals went up when all the factors enumerated seemed to point to the 
probability of a downward movement, and there were also a few animals 
which went down when the mechanical difficulties were such as should 
have impelled them upward. As previously noted, the upward-moving 
animals sometimes displayed an unusual amount of activity, and the ex- 
ceptional cases of positive geotaxis in the negative group were those of 
animals usually slow and stupid. As the effort was constantly made to 
select only fairly active animals in good condition for producing mucus, 
there were not many of these exceptions. Knowing the habits of the 
animal, we may naturally associate its activity with its food condition. 

The question then comes up, Does the state of the animal's nutrition 
affect its tendency to move toward the earth ? Does a poorly nourished 
animal respond to the stimulus of gravity differently from a well-nour- 
ished individual ? To get an answer to this question, four animals were 
put into a small box which contained nothing but moist earth. The slugs 
were kept there for three days, and a series of geotactic tests was then 
made upon them. Two of the four individuals were inactive, aud so un- 
satisfactory in response that no series was obtained. The other two were 
rather restless, but precise in response. All the animals were then 
returned to the box and supplied with fresh cabbage leaves. The next 
morning another series of geotactic stimuli was given. The rather 
meagre results given in Table IX. are perhaps not worth very much, since 
only one individual (No. 1) out of the four responded well in both cases. 

The ratios given in the second column (Table IX ) indicate that 
slugs Nos. 1 and 2 belong with those of the positive half of Col. 8, 
Table IV. I unfortunately neglected to control these experiments by 
observing the geotaxis before the animals were deprived of food. In 




Comparison of Kesponses of Individuals when poobly nourished and 

when well nourished. 



Ratio of Anterior 

to Posterior 


Poorly nourished. 

Well nourished. 

No. of Trials. 

% Geotaxis. 

No. of Trials. 

°1 Geotaxis. 




















both instances (Nos. 1 and 2) the animals were rather dry, and they 
were not noticeably different in this respect after being well fed. No. 2 
was less active and less precise in response after it had had plenty of 
food. I think these experiments too few to warrant laying much stress 
upon them, but I have given them here because they at least point in the 
direction of what we might reasonably expect, since the natural desire of 
the animal to escape from its narrow prison and the impulse to seek 
food would both tend to make it go up, if given the opportunity. 

Another element which may alter the slug's inherent geotaxis is 
probably the state of fear. This element may be combined with the 
impulse to seek food, as is perhaps the case in the instances just given, or 
it may operate by itself. Animals which had just been captured were al- 
ways kept in a small tin box. The captured animals would thrust them- 
selves between the box and lid, which was not perfectly tight, in their 
endeavors to escape, and they had to be frequently pushed back. When 
they were transferred to the large box mentioned at page 187, it was 
always found that they had all collected in the upper part of the smaller 
box. This may have been solely for the purpose of getting air, but such 
animals put on a glass plate were exceedingly active and restless, and 
usually exhibited a decided negative geotaxis. I have not made any care- 
ful set of experiments to find out whether these negatively geotactic 
animals afterwards became positive. In one instance, I confined over 
night in a small flower-jar a slug (not a freshly captured one) which had 
shown a very decided positive geotaxis. In the morning it was found at 
the top of the jar, and, when placed on a glass plate, showed great activ- 
ity, as though it sought to escape. In every one of the tests which I 
then made, it responded negatively. From these few observations, it 


would seem that fear, by impelling the animal to escape from captivity, 
may alter its geotatic response. Such freshly captured slugs, moreover, 
which seem unusually restless and excited, respond more capriciously 
to the stimulation of light, as some later experiments will show. 

Summary of Part II. 

The results of the foregoing experiments warrant the following con- 
clusions : — 

1. On an inclined glass plate, all slugs give a geotactic response. 

2. Certain slugs give a decided positive, others a markedly negative 
geotactic response; a few are somewhat indifferent. 

3. The geotaxis of animals kept in confinement does not vary much 
on different days, nor at different times on the same day. 

4. The occasional vagaries in the responses of individual animals are 
to some extent due to thigmotactic and phototactic influences. 

5. The different geotactic response, on a glass plate, of different indi- 
viduals is due mainly to two factors : (a) The quantity and quality of the 
slime secreted, which is a very important factor ; (b) the relative pro- 
portions of the length of the anterior and the posterior regions of the 
animal's body. All the conditions being the same, it is this factor 
which " determines whether the head end will be directed up or down." 

6. If the ratio of length of anterior to posterior region of body is 2:3, 
or more, and the mucus is of good quality and sufficient quantity, the 
slug will be positively geotactic. 

7. If the ratio is 3 : 5, or less, the animal will usually migrate upward, 
and the nearer the ratio approaches 1 : 2 the more apt is the slug to 
respond negatively. 

8. In a small number of individuals, in which the ratio lies between 
2 : 3 and 3 : 5, the response will depend largely on the condition of the 
mucus and cooperation of other factors. 

9. All slugs have a natural tendency to move towards the earth. 
This tendency is masked in the animals which are negatively geotactic 
on a glass plate by the greater pull of gravity on the disproportionately 
larger and heavier posterior region of the animal. 

10. The general downward tendency may vary normally at different 
times of the day, owing to the animal's habit of remaining in concealment 
in the daytime and feeding at night. 


III. Phototaxis. 

The influence of light on the direction of locomotion has been very 
generally noticed among organisms, even the mostly widely separated. 
The swarm spores of many algae, desmids, and other lowly organized 
plants, are as truly responsive to light stimuli as are crustaceans or verte- 
brates. According to the character and direction of the stimulating 
light rays, two kinds of light responses have been distinguished. Photo- 
taxis is the response with reference to the direction of the rays of light. 
The organism moves in the path of the ray, either positively (toward) 
or negatively (away from it). The response to different intensities of light 
from which the directive force of the rays has been eliminated is known 
as photopathy. A photopathic animal is one that selects, out of a series 
of uniformly increasing intensities of light, a limited field of a certain 

Some animals, like butterflies and fresh-water Entomostraca, are 
strikingly positively phototactic to diffuse daylight ; others, such as the 
earthworm and the leech, are as pronouncedly negative. The kind of re- 
sponse (positive or negative) may be different in closely allied forms and 
in different stages of development of the same species. For example, 
butterflies are attracted by strong sunlight, while moths are repelled 
by it. The adult house fly is positively phototactic to daylight ; its 
larva, negatively (Loeb, '90, pp. 69-77, 81-83). 

The phototactic sense has been shown in some forms to change with 
different intensities of light. Thus, Famintzin ('67) found that swarm 
spores positively phototactic to a certain intensity of light became 
negative to a light of greater intensity. The same phenomenon has 
been found true of various flagellates, desmids, diatoms, oscillariae, etc. 
Wilson ('91, p. 414) found that Hydra fusca was attracted by diffuse 
daylight and repelled by strong sunlight. Finally, the moth's liking 
for candlelight and aversion to daylight is well known. The fact 
that many organisms are photopathic — that is, have a preference 
for light of a certain intensity — makes it probable, in connection with 
these observed variations in phototactic responses, that, for most organ- 
isms, there is an optimum intensity to which they will respond posi- 
tively. This optimum will vary widely in different species, probably 
according to the habits and the usual environment of the species. In- 
habitants of sunny pools or the open air will have an optimum of rela- 
tively high intensity ; those which dwell in the ground or in shady places 


will have a correspondingly lower optimum. May it not be that every 
organism will respond positively to a certain range of light intensities and 
negatively to another range of intensities which is greater ? The nature 
of the phototaxis may sometimes be gradually changed by organisms 
becoming acclimated to new conditions. Verworn ('89, pp. 47-49) found 
that a culture of the diatom Navicula brevis, which ordinarily is negatively 
phototactic to very weak light, became positively phototactic when reared 
for several weeks near a window. Groom und Loeb ('90, pp. 166-167) 
found that young Nauplius larvae of Balanus which were at first positively 
phototactic to daylight became negatively phototactic later in the day, 
probably as the result of the accumulated effects of this exposure. 

The character of the light responses, as was the case with geotaxis, 
depends also to a certain extent on other external conditions, such as 
those of temperature, the states of density and pressure, and various 
chemical influences. Polygordius larvae, when gradually cooled from 
16.5° C. to 6° C, were found by Loeb ('93, pp. 90-96), to change from 
a negative to a positive phototaxis. Like results were obtained by him 
from Copepoda. When the temperature was raised from 6° C. to 16° C, 
the animals again became negative. Increasing the density of sea-water 
by the addition of sodium chloride produced a change from a negative to 
a positive response, thus acting like diminished temperature. Engelmann 
('82, pp. 391-392) showed the apparent phototactic response of chlor- 
ophyllaceous ciliates to be really a chemotactic attraction for oxygen, 
which chlorophyll can produce only in the light. These facts make it 
important in any study of light response to consider other possible influ- 
ences, and above all to take account of the strength of the stimuli used. 

Davenport and Perkins ('97) found that the slug (Limax maximus) 
responded with marked precision to the varying stimuli of gravity at 
different angles of inclination of the glass plate. The precision of re- 
sponse varied correlatively with the force of gravity. In fact, the paral- 
lelism was almost perfect. The question naturally rises, Is there a 
similar parallelism between other stimuli and their responses ? 

A very little experimentation shows that the slug is extremely sensi- 
tive to light. We have already seen how light may enter in to modify 
the action of gravity. Casual observation shows that the response is in 
most cases negative, — the animal moves away from the source of 
light. Owing to its method of locomotion, the slug is easily experi- 
mented on. It moves slowly and deliberately. In regard to its responses 
to light, the following questions suggest themselves : (1) Are all indi- 
viduals negatively phototactic to artificial light? (2) Does the precision 


of response vary correlatively with the intensity ? (3) Within what 
limits of intensity is the animal responsive ? (4) Does the kind of 
response vary at different intensities ? (5) Is there a difference in the 
sensitiveness to light of the two sides of the animal's body ? (6) In what 
part, or parts, of the animal's body does the sensitiveness reside? (7) 
How does the animal move when in the dark and deprived of all stimu- 
lating influences ? These various problems came up gradually as the 
work progressed and were considered in turn. Other interesting studies 
have suggested themselves in the course of the investigation, but there 
has not been time to go much beyond a consideration of the questions 
above proposed. The experiments performed were all phototactic ; that 
is, they were studies of the response of the slug to the direct rays of 

Methods. — The methods used were simple. For light, the standard 
candle and the ordinary small Christmas candle, of a one fourth candle 
power, were employed. The candle was placed in a box 50 cm. (20 
inches) high and having a bottom 12.5 cm. (5 inches) wide and 20 cm. 
(8 inches) long. It could be raised or lowered to any desired position by 
means of an adjustable stage inside the box. A circular opening in the 
middle of one of the broad sides of the box 2 cm. (£ inches) in diameter 
permitted the light to pass out. This opening was covered by a piece of 
oiled paper, so as to give a well-defined uniform source of light. During 
the experiment the box was closed by a lid. The intensity of the light 
was varied by altering the distance between the box and the animal. 
Additional thicknesses of paraffined paper were also employed when it 
was desired to greatly diminish the intensity of the light. The animal 
was put on a circular glass plate which rested horizontally on a support, 
and the box was raised so that the centre of the light opening was in the 
same horizontal plane as the body of the animal. The movement of the 
slug from its original position was measured in degrees in the following 
manner. A circle of the same size as the glass plate was described on a 
sheet of thin paper and divided by radii into 72 sectors of 5° each. This 
sheet was pasted to the under side of a second circular glass plate (of the 
same size as the first), on which also a heavy base line was drawn, corre- 
sponding with a diameter of the circle. This second plate was so placed that 
the centre of the source of light was on a line perpendicular to the base 
line at its middle point. The slug was put on the first glass plate, which 
could be rotated so as to bring the animal into any desired position with 
reference to the base line. The experiments were carried on in a dark 
room provided at one end with a hinged window which could be easily 


and quickly thrown open. The window was covered with a thick, black 
cloth, so that, when closed, external light was almost completely shut off. 
Unfortunately, it was impossible, owing to the position and nature of the 
room used, entirely to equalize all conditions. The temperature was not 
the same from day to day and varied somewhat in different, parts of the 
room. Generally, it was so hot and close that it was necessary to leave 
an opening between the sashes, and this of course created a slight draft 
and produced irregularities of temperature. No account was taken of 
the varying humidity of the atmosphere, a factor which may have some- 
what influenced the animal's locomotion. Moreover, as the room was 
not perfectly light-tight, there were feeble light stimuli in addition to the 
artificial ones used. However, all these imperfections were but slight, 
and, since they entered more or less into all the experiments, could not 
greatly alter the relation between the results, which was the main thing 
sought in the investigation. Other unestimated possible influences were 
the nutrition of the animal and such slight thigmotactic stimuli as could 
not well be avoided. 

The strength of the different intensities of light used was measured by 
moving a piece of paper, the centre of which was oiled, between a light 
of known intensity and the light whose intensity it was desired to know, 
until the oiled spot on the paper was not distinguishable from the rest of 
the paper. The distance from this point to each source of light was then 
measured. Since the intensity varies inversely as the square of the dis- 
tances, it is an easy matter to calculate the relative strengths. This 
method is accurate enough for all ordinary purposes. 

Operations and Results. — In beginning any experiment, the slug, as 
soon as it had definitely orieuted itself, was rotated into such a position 
that the axis of its body coincided with the base line, and its head was at 
the centre of the disk. The window was then immediately closed and 
the time noted. At the expiration of 45 seconds, the window was thrown 
open and the animal's position instantly noted. The extent of positive 
or negative migration was at first ascertained by finding the length of the 
arc stretching from the base line to the radius which was parallel tvith 
the axis of the slug's body. Any movement into the half of the circle 
toward the source of light was called positive ; any movement into the 
other half, negative. It would occasionally happen that an animal would 
at first move into the positive half of the circle and then turn away from 
the light. In this case the axis of orientation made a negative angle 
with the base line, although the animal itself lay in the positive half of 
the circle. Later, in the course of the experiments, the positive or 

vol. XXXVII. — 14 


negative movement of the animal was measured by taking the radius 
which passed midway between the two tentacles, without regard to the 
position of the body axis. A comparison of the two methods showed but 
little difference in the results. The animals only occasionally made these 
irregular responses, first in a plus and then a minus direction. As a rule, 
the migration was unequivocal after the head end had oriented itself to 
the stimulus. Experiments were made with 18 different intensities of 
light, each constituting a " series." Six successive observations were 
made on each individual (3 with the right side exposed ; 3 with the left), 
and from 8 to 14 animals were employed in each "series." i.e., at each 
intensity of light, making a total of from 48 to 84 observations at each 
candle power used. A summary of the results for each of 18 such 
" series " is given in Table X. 

The first column gives the number of the series ; the second, the 
intensities of light. This intensity is expressed in terms of the standard 
candle power at a distance of one meter. The next column (3) shows 
the total positive migration of the (8 to 14) animals experimented with. 
Column 4 similarly gives the total negative migration. Column 5 repre- 
sents the average arithmetical angular deviation from the original posi- 
tion due to phototactic stimuli, effected in a period of 45 seconds by all 
the slugs, without regard to the positive or negative character of the 
individual phototaxis. This average was obtained by adding together the 
average phototactic responses (whether plus or minus) of each individual 
of the series and dividing the result by the number of animals. The 
average plus or minus phototactic response (algebraic average) for each 
series (column 6) was obtained by getting the difference between the 
sums of all the plus and all the minus movements of each series and 
dividing this difference by the number of tests (observations) made. 
Column 7 gives the number of positively phototactic animals in each 
series; column 8, the number of negative animals; column 9, the num- 
ber of indifferent animals ; and column 10, the total number of individ- 
uals employed in each series. The sequence of the series is not the 
same as that of the experiments, but is based on gradually diminishing 
light intensities. I did not determine the possible influence of the heat 
of the candle for each of the series, but in one series of experiments in 
the dark (186), a candle, covered (to shut out the light) with an opaque 
paper of the same thickness as the paraffined paper, was left burning at 
a distance of 30 cm. (intensity .676 C. P.). 

A casual glance at the table at once answers the first of the questions 
proposed in the statement of the problems (pp. 207-208). All slugs are 




not negatively phototactic. At the strongest intensity of light used, two 
animals exhibited a positive phototaxis, — they moved toward the stiinu- 

Responses of the Slug to Light. 











No. of 

Intensity of 

Total Pho 
gration i 

;otactic Mi- 
i Degrees. 

Average Response 

in Degrees in a Period 

of 45 Minutes. 

No. of Animals. 

rical .Sum. 























































- 5.1 









- 6. 










+ 1.4 









+ 3.5 










+ 7.9 









+ 1-7 









+ 8.3 


















+ 4.2 

















+ 2. 




























+ 7.2 


















+ 1. 









+ 1-2 






" with 
candle heat. 




- 3. 





lating light rays. Here, then, arises another problem, similar to the 
one treated of in the first part of this paper, viz., What determines 
whether a particular slug shall be positively or negatively phototactic ? 
In the first series of experiments — in fact throughout this whole set — 
the animals used were about equally divided between large, small, and 
medium-sized individuals. The two positive animals in series 1 were both 
of large size. They were very active. The only peculiarity wherein 
they seemed to differ from other individuals was in the unusually 
sticky character of the slime. Whether there is any correlation between 
this fact and the liking for strong light, I am not prepared to say; It 
is possible — and certain observations seem to indicate that it is highly 
probable — that the food conditions of the animals have some influence 
on their responses to light, as they were shown to have on their responses 
to gravity. The psychic state of the animal is also to some extent, I 
think, a factor. Freshly caught slugs when put on a glass plate some- 
times acted as if in great fear. They displayed unusual activity and 
were very erratic in their movements. If forcibly checked or held, 
they made strenuous efforts to escape. The great activity of the posi- 
tive individuals indicates a possible state of fear. One animal in par- 
ticular seemed highly abnormal. Several times it moved directly toward 
the circular field of light and even placed its tentacles against the oiled 
paper which covered the opening. This was the only individual in the 
whole course of the experiments which exhibited a response like that of 
moths. No definite set of experiments was planned or carried out in 
regard to this matter. 

As we run down column 5, we see that the average arithmetical 
response varies quite strikingly at the different intensities. The first 
seven series show a gradual decrease in the average response as the 
strength of the light is diminished. Although not so regular, there is 
also a gradual decrease in the degree of negative response on the part 
of these seven groups of animals, as shown by the average algebraic sums 
of their responses (column 6). 

Owing to the constant dying off and deterioration of the stock, it was 
found impossible to use the same set of animals in all the different series 
of experiments. Moreover, this was not desirable, for the reason that 
an animal which is constantly experimented on gradually loses its sensi- 
tiveness, and thus its responses become untrustworthy. Not knowing 
the factors which determine the kind of phototaxis, it was of course 
impossible to make a uniform selection in this respect. We see, how- 
ever, that the number of negative animals (column 8) is less at the 


weaker intensities than at the stronger. When we come to series 8 of 
the table, we meet with a new condition of affairs. Instead of a still 
further decrease in the amount of deviation, there is a sudden slight in- 
crease, from 9.1° to 13°, and a reversal in phototaxis for the series from 
an average response of — 6° to + 1-4°. The number of positive indi- 
viduals has increased from 3 to 7. It was because of this striking 
change that it was thought best to repeat this series and the three suc- 
ceeding ones on another set of animals. The absolute positive or nega- 
tive migration was this time taken without regard to the position of the 
body axis. Series 7a, 8a, 9a, and 10a are hence taken at the same 
intensities as 7, 8, 9, and 10 respectively. These repeated series indi- 
cate as strongly as the first set that an intensity of .001,69 C. P. very 
nearly marks the lower limit of negative phototaxis in the slug. Some- 
where near a candle power of .000,754, lies an intensity which attracts 
about as many animals as it repels and in about the same degree. That 
is, the average phototaxis (algebraic sum) is zero. Below this intensity, 
there is more attraction than repulsion, and hence there is an average in- 
crease of migration toward the light. The table shows that the average 
positive response increases to some extent correlatively with the diminution 
of the light intensity, up to a certain point. This point, according to 
the results here obtained, is the intensity of .000,022 C. P., where 
the average movement toward the light, in a period of 45 seconds, was 
through an angle of 22.3°. As we go below this intensity, there is 
again a falling off in the strength of the positive response, which dimin- 
ishes, however, with a good deal of irregularity until absolute darkness 
is reached. These facts will become more apparent from the study of 
their graphic portrayal in the curve here given. 

The continuous line represents the curve as plotted from the results of 
Table X., column 6 ; the dotted line, the curve of responses as one may 
assume theoretically it would have been, could all of the conditions 
other than intensity of light have been equalized. The abscissae here 
represent the logarithms of the intensities of light + 10. Beginning 
with darkness on the left end, there is a constant increase of intensity 
as we move toward the right. The sines of the angles of response are 
marked off on the ordinates. Remembering that the left represents a 
region of weak intensity and the right a region of strong light, that all 
points above the line x x' are points of positive response and all points 
below it of negative response, we can understand the significance of 
the curve. In the region of strong light, the curve lies far below the 
line x x', but gradually rises toward and finally crosses it, as the light 












/ / 




















\ ? 






















> 1 : 




3 a 




U . 




















)a* J 




7 a 



, 7 



1 1\ 

















i \ 






■^ / 







\ * 











i l 

i 1 




Figure 2. 

Curve of Responses to Light Abscissae are logarithms of light intensities plus 
10 ; ordinates are sines of angles of responses multiplied by 10. 


diminishes in strength. Then there is a gradual increase in positive 
reaction, which reaches its height in a response of +22. °3 at a .000,022 
C. P., and then falls toward the zero line as we approach darkness. 
There is some irregularity in the negative region, but on the whole the 
rise is gradual. In the region of positive response, there is a consider- 
able lack of regularity, especially marked by the interpolation of one 
series (12) of very low response between the two series of greatest 
response. These series intermediate between Nos. 11 and 16 represent 
later experiments than the two series bearing those numbers. Having 
obtained such a marked positive response at two widely separated in- 
tensities of light, it was thought desirable to get other intermediate 
series. Hence, the order of the series as arranged in the table, on the 
basis of gradually diminishing light intensities, does not, as already stated, 
represent the order in which the series were obtained in my experiments. 
While the slugs, thus far, had, on the whole, been in good active condi- 
tion, they were not so in these intermediate series. Although a fresh 
supply was obtained, all the animals seemed much more stupid and 
irresponsive than usual. Some of them refused to move, when put on 
a plate, and many of those that did, responded in a very half-hearted 
way. The cause of this unusual lack of activity, I could not discover. 
It may be that a slight change in the food of the animals, which I made 
at this time, was partly responsible. At any rate, instead of obtaining 
responses intermediate in amount between those of series 11 and 16 as 
might have been expected, the results were as have beeu given. Series 
12 was the last one taken. In this, the animals were noticeably more 
stupid and irresponsive than in any of the preceding experiments. It is 
very evident from these results, I think, that the precision of response 
will vary to some slight extent from day to day. The negative responses — 
those to strong intensities of light — will not be as variable at different 
times as the positive responses — those to weaker stimuli — as the curve 
shows. The varying thermal conditions of the room, already mentioned, 
may have been in part a cause of this irregularity. Furthermore, an 
animal that has had plenty of food is likely to be stupid and slow in 
movement and is more apt than a hungry one to seek darkness and 
concealment. On the other hand, a hungry, active slug will probably ex- 
hibit positive phototaxis in a most marked and sometimes abnormal degree, 
as was the case occasionally with the positive animals at the strongest 
light intensities. Besides this individual variation, there is, I think, a 
general variation for all slugs from time to time, for reasons imperfectly 
known, which will find its expression in curves of different heights. 


Thus the less responsive animals of the intermediate but later series 
mentioned fall into a less prominent curve, as is indicated by the shorter 
dotted line in the diagram. The curve of positive response approaches, 
but never actually reaches, the zero line. Even in darkness there is a 
slight positive migration. This series (No. 18a) represents the average 
of two series of experiments, one of 54 and the other of 66 deter- 
minations, each taken at different times during the investigation. This 
slight positive response — speaking of it as positive with reference to the 
position of the source of light in the preceding series (17) — may be inde- 
pendent of conditions of light and due to several causes. As mentioned 
before, the thermal conditions of the room were not uniform, conse- 
quently the positive response may have been a response to heat. The 
movement was away from the window and hence might be ex- 
plained as a negative response to the repeated inflowing of daylight, 
when the window was thrown open to make observations. In the last 
few experiments an opaque screen was put up between the animal and 
the window. In these cases the average of the responses was slightly 
negative, so there is some reason to suppose that it was in part the posi- 
tion of the window in the previous experiment that determined the slight 
positive migration. The actual phototactic responses to the caudle light 
in the positive half of Table X. would then be the observed responses 
minus this small positive movement in the dark. The actual negative 
responses to the strong intensities would be the observed responses plus 
this increment. In series 18b the box was placed at a distance of 
30 cm. (C. P. 0.676) with the light burning, but the opening was cov- 
ered with a piece of black paper to shut out the influence of the light 
while leaving that of heat. The small average response of —3.0 may 
possibly be regarded as a thermotactic one, and, if so, will have to be 
deducted from the negatively phototactic response to this intensity of 
light. For intensities less than the 0.676 C. P., the response to the heat 
would be correspondingly less. 

We can now answer the second and fourth questions (pp. 207-208) by 
saving, — that the precision of the phototactic response does, on the 
whole, vary correlatively with the intensity of the light, and that the kind 
of phototaxis (positive or negative) is not the same for different intensi- 
ties of light. The slug gives a negative phototactic response to strong 
light, a positive one to weak intensities, and is neutral to an intensity 
somewhere between the extremes. 

A few individuals were tested successively at different light intensities 
in order to find out with what precision an individual's phototaxis might 
vary with a change of intensity. 



Responses of Individuals to Different Intensities of Light. 

Animal No. 









.382 C. P. 

.382 C. P. 
.382 C. P. 


.169 C. P. 
.169 C. P. 
.169 C. P. 


.067 C. P. 
.067 C. P. 

.067 0.1'. 

- 10° 


In all these cases, there if seen to be a gradual diminution in the degree 
of response as the intensity of light diminishes. Again, from an animal 
which responded negatively to a certain intensity of light, a positive 
response could be got by weakening the light sufficiently (Nos. 2 and 3, 
Table XII.), and a positive animal could be made to give a negative 
response by using stronger light (No. 1, Table XII.), as the following 
instances show. 

Responses of Individuals to Different Intensities of Light. 











.382 C. P. 





.676 C.P. 


.0424 C.P. 



.169 C.P. 



- 2.°5 

.0067 C.P. 


.0047 C.P. 


No. 3, Table XII., shows a less regular response than any of the other 
animals. From a response of — 37° it drops to one of — 2.5°, and, under 
the influence of a still lower intensity of light, it again rises to a marked 
negative response of —32.° At a still lower intensity, it gives a striking 
positive response of +36°. Here, however, we have well illustrated in 
particular individuals the law laid down for all slugs, — that they are 
negatively phototaetic to strong intensities of light, the precision of re- 
sponse varying correlatively with the intensity of the stimulus ; that to 
weak intensities they are positive ; and that to a certain intermediate 
intensity they are neutral. 

A glance at the intensity column (Table X.) shows that the slugs are 



responsive to a very wide range of intensities. They would probably 
continue to respond negatively to still stronger light, until the light 
became strong enough to kill the animal. They respond positively to a 
light (series 16) less than one three millionth part as intense as the 
strongest intensity experimented with. The response to the weakest 
intensity used (series 17) is less than the positive migration in the dark. 
Hence we cannot speak of this as a phototactic response. This attenua- 
tion of light was so weak that I could not be sure I saw it myself, and 
had constantly to reassure myself by approaching it. The slug is evi- 
dently sensitive to a very minute degree of light. 

Where does the slug's sensitiveness reside? The first and most 
natural answer is, that the eyes are the important organs. The matter 
was tested on five different individuals. The normal phototactic response 
was first taken with a .676 candle power. Then the dorsal tentacles, 
bearing the eyes, were snipped off with scissors and the animal again 
experimented on. The results are given in Table XIII. 

Effect of Amputation of Tentacles. 


Normal Phototactic 

Response after Amputation 
of Dorsal Tentacles. 

Ventral Tentacles also 






- 3.° 










+ G.° 

As soon as the operation was performed, the stumps were retracted, as 
the tentacles are when stimulated by touching, or by strong light. After 
a moment or two, the animal again rolled out the stumps and began 
moving forward in perfectly normal fashion, as though nothing had 
happened. The only observable difference was a perhaps slightly in- 
creased activity. This table (XIII.) shows a striking effect of the 
amputation on the phototactic response. In some cases, the animal 
deviated but very little either positively or negatively from its original 
position, but kept on moving ahead in a straight line. In other cases, 
the amputation seemed to cause a change from a strongly negative to a 



more or less positive response. In the case of animal No. 3, removal of 
the eyes did not seem to altogether prevent, though it considerably 
reduced, the negative response. Thereupon, the ventral tentacles were 
also amputated and the result then was a slight positive response. Since 
there is probahly some shock to the nervous system by the amputation, 
these results ought to be corroborated by other experiments where the 
eyes are covered over with some substance to shut off the rays of light. 
This, I have not yet succeeded in doing satisfactorily. 

The experiment of removing only one of the ocular tentacles was tried 
on two different animals with the following interesting results. 


Comparison of Effect of Amputation of Right and Left Dorsal 



Normal Phototactic 

Response after Amputation of 

Right Tentacle. 

Left Tentacle. 





In the case where the right tentacle was removed, the animal still 
responded negatively with considerable precision. Amputation of the 
left tentacle, in the case of No. 2, on the other hand, resulted in a slight 
positive phototaxis. While these two cases by themselves have little, if 
any, significance, taken in connection with facts now to be discussed, they 
seem to indicate a greater degree of sensitiveness to strong light on the 
part of the left side of the animal's body than the right. 

It will be remembered that our thigmotactic experiments pointed to a 
possible asymmetry in the sensitiveness of the right and left tentacles of 
the slug. Do we find a similar asymmetry in the responses to light? 
Table XV. gives the responses of right and left sides respectively for the 
18 series. Column 1 gives the number of the series, column 2 the in- 
tensities of light, columns 3 and 4 the total angular migrations in a positive 
and negative direction for the series when the right side was exposed to the 
light, and the fifth column the algebraic average (positive or negative) 
phototactic response of the right side. Similarly, the next three columns, 
6, 7, and 8, give the responses of the left side. Column 9 represents 
the total movement of the series in degrees to the right. This result was 
obtained by adding the total positive responses of the right side (column 3) 



Comparison of Responses of Right and Left Sides to Light. 



















& s 


Intensity of 

Responses of Right 
Side in Degrees. 

Responses of Left 
Side in Degrees. 

Total Movement 
in Degrees to 




+ or — 



+ or — 




























- 4.3 











- 3.3 














- 8. 











+ 6.7 








- 8.3 



- 3.9 








- 1.4 



+ 4.1 








- 3. 











+ 6.3 



+ 9.6 








+ 12 



- 5. 








+ 8.1 



+ 8.5 



















+ 9. 



- 0.7 


















- 3.8 



+ 7.6 











+ 9. 



















+ 2.5 






















- 0.2 



+ 2.6 







" with 
candle heat 







+ 7. 












" less 18a & 186 









and the total negative responses of the left side (column 7), — these 
responses being necessarily right-hand movements. The total movement 
in degrees to the left (column 10) was likewise obtained by adding the 
total negative responses of the right side and the positive responses of the 
left side. Column 1 1 gives the total number of animals used in each series. 
In the region of negative phototaxis, the total positive and negative 
angular migrations, and the average negative phototaxis of all the series 
(1-7, inclusive) when the riglit and left sides respectively were turned 
toward the light, were as follows. 


Sum of the Responses of Right and Left Sides when Phototaxis 

is Negative. 

Side turned 
toward Light. 

Total Angular Migration. 

Average Negative 







This shows on the whole a less sensitive right side, or, to put it differently, 
a more marked negative phototaxis of the left side. How is it when the 
animals become positively phototactic ? Table XVII. gives the average 
positive response of the right and left sides for series 8 to 18, including 
series la, 8a, da, and 10a. 


Sum of Responses of Right and Left Sides when Phototaxis 

is Positive. 

Side turned 
toward Light. 

Total Angular Migration. 

Average Positive 








Here an asymmetrical response is less strongly marked. The left side, 
however, appears on the average to be somewhat more strongly attracted 
toward the light. The results prove that the asymmetry in response of the 
right and left sides cannot be wholly due to a tendency to move toward 


the right, for, if this were so, we should expect an average positive 
response of the right side as much greater than that of the left side, as the 
average negative response of the left is greater than that of the right side, 
for both these would mean a greater movement to the right. These 
facts curiously suggest that the right and left sides are attuned to slightly 
different intensities of light. Is this possibly due to ancestral habits of 
life in which environment, acting unequally on the two sides, produced 
this difference ? 

The results obtained for the right and left sides from the experiments 
in darkness (series 18a) are rather puzzling. If the responses are due 
to some uncontrolled directive stimuli of the kind already suggested, it 
would seem that the two sides had given opposite responses. As these 
experiments represent two series taken at different periods, it is the 
more surprising that they should both show this peculiarity. Again, in 
the responses to weak candle heat (series 18b) the left seems to have 
been positively, and the right side negatively affected. So far as is known, 
there was no unequal operation of stimuli on the two sides. 

Related to this matter is the question, — Is there any tendency on the 
part of all slugs to move either to the right or to the left? Individuals 
were noticed which seemed to have a marked tendency to continue 
moving toward the right, and there were others which seemed to be as 
strongly biassed toward the left. Not many seemed entirely indifferent. 
The total movement of all the slugs in the region of negative response 
(series 1-8, Table XV.) toward the right side was 8786° (col. 9), and to 
the left G471° (col 10). In the positive region (series 8-18, Table XV.), 
the total migration toward the right side was 8540° (col. 9), and to- 
ward the left 8568° (col. 10). Thus, there seems to have been con- 
siderably less migration toward the left in the range of negative 
responses, but only a slightly greater movement toward the left in 
the region of positive response. In all the 17 series, there was a mi- 
gration towards the right of 17,326°, and towards the left of 15,039°. 
That is, there appears on the whole to have been a slightly greater 
average movement for all slugs toward the right than there has been 
toward the left. What do we find to be the case with the animals experi- 
mented on in the dark? Out of the 120 determinations made on 20 
animals in the dark (series 18a), the amount of right-hand movement 
was 2270° and the left-hand movement only 4 G0°. That is, there was 
nearly five times more migration toward the right than there was toward 
the left. In series 18b, however, there seems to have been a marked pre- 
ponderance of movement toward the left. From the foregoing experi- 


ments, it seems pretty clear that there is a difference in the sensitiveness 
of the right and left sides. There is also some indication of a slightly 
greater average tendency to move to the right. But a further study of 
the undirected movements of slugs in the dark is needed. 

Studies have been made by several observers on the undirected move- 
ments of a number of different animals, chiefly ants and other insects. 
In all animals experimented on, there appears to be a tendency to travel 
in loops or constantly widening spirals. Man, when he loses his way, 
travels in a circle. Some interesting observations have been made bv 
George and Elizabeth Peckham ('98, pp. 211-219) on the sense of 
direction in the solitary wasps. When the wasp starts out from its nest, 
it flies quite around it and gradually circles farther and farther away in a 
constantly enlarging spiral, sometimes recrossing its path a number of 
times. The authors' observations show that this action is to enable the 
wasp to familiarize itself with its surroundings, so that it can find its way 
home when it so desires. The similar phenomenon observed in other 
insects, such as ants, is, no doubt, for the same purpose. Davenport 
('97, pp. 278-279) in his experiments on Amoebae found that, when 
their movement was undirected by any external stimulus, they tended to 
travel in curious spiral loops. Pouchet ('72, pp. 227-228) made obser- 
vations on the movement of larvae of Musca (Lucilia) caesar in the dark. 
There is a striking contrast between the paths given by him of the un- 
directed movements and those made in response to the stimulus of light. 
The tendency to travel in a gradually widening spiral has also been 
observed by the writer in young frog and toad larvae — before the develop- 
ment of mouth and eyes — when they are dislodged from the support to 
which they are clinging. 

Most of the following experiments on the slug were made in a room 
about 12 feet square. The floor was sometimes covered with cardboard 
or paper, but in other experiments was left bare. Heavy curtains were 
hung in front of the windows and light shut out as completely as possible. 
The experiments were conducted at night, and the temperature of the. 
room was nearly, if not quite, constant. A slug was put on the floor in 
the centre of the room and left to itself for two or three hours, sometimes 
longer. By means of the mucous secretion, which hardened into white, 
shiny flakes, the exact path of the animal could, in most cases, be easily 
followed. This path was roughly reproduced by pencil on paper. A num- 
ber of these paths are given in Figures 3-22, much reduced from the 
actual space covered. The series here given includes all the animals 
experimented on, with the exception of three individuals which did not 



Figttres 3-22. 
Much reduced copies of the tracks made by slugs (Limax maximus) in the dark. 
dx., right-hauded loops ; s., left-handed loops. 


give any characteristic paths. Two of the three moved only a short dis- 
tance in wavy lines without recrossing their paths, and were in poor condi- 
tion, for they did not go far, and shortly died. One extremely active little 
individual moved ahead in a straight line quite across the floor, a distance 
of eight or ten feet. With these few exceptions, it will be seen that 
there is a very marked tendency to travel in loops. In general, the 
loops varied in size from a couple of inches in diameter to two feet and 
sometimes more. The animal generally makes a circle soon after starting 
out, and then may travel for some distance before again recrossing its 
tracks. The individuals which did the most looping also showed a 
tendency, by gradually swinging away from the starting point, to make 
larger and larger circles. Nos. 7, 8, 11, 13, 14, 16, 17, 19, and 22 all 
showed this tendency. The smaller individuals usually make the 
smaller loops, but this is not always the case. Although the paths made 
by different animals have a very different appearance, they all show the 
same general looping tendency. It will at once be noticed that all curves 
are not in the same direction. Some are right-handed loops, others are 
left-handed, and two cases, Nos. 10 and 12, contain loops of both right and 
left hand character, or at least indicate a tendency to the formation of 
such loops. As a rule, however, the individual shows a marked con- 
stancy in the character of the loops made. Disregarding the two cases 
in which there were both right and left hand loops, we have ten individuals 
with a tendency to circle to the right and eight individuals with just as 
marked a tendency to circle to the left. This does not indicate a very 
great preponderance of individuals travelling to the right. If the total 
space travelled over by all individuals be considered, I think it might 
show, on the average, a more marked swerving to the right than does a 
counting of right and left circling individuals, but I have not measured 
the distances carefully enough to speak confidently on this point. The 
evidence thus far accumulated in regard to an asymmetrical response of 
the right and left sides to artificial stimuli points to a greater sensitive- 
ness of the left side, which is perhaps correlated with a slight average 
tendency to move toward the right side more than to the left. 

Summary of Part III. 

These studies on the light responses of Limax maximus seem to estab- 
lish the following points: — 

(1) The animals are markedly phototactic. 

(2) There are individual differences in phototaxis, as there are in 

vol. xxxvn. — 15 


(3) To strong light, slugs, on the average, give a strong negative 

(4) The degree of response gradually diminishes with the reduction 
in the strength of the stimulus. 

(5) There is a certain strength of light which appears neither to repel 
nor attract the slug. This may be said to be a neutral stimulus. 

(6) Reduction of the intensity of the light beyond the neutral point 
changes the phototaxis from negative to positive. 

(7) The positive response becomes stronger up to a certain degree of 

(8) It then gradually diminishes with decreasing intensity until abso- 
lute darkness accompanied by no response is reached. 

(9) Slugs are responsive to light stimuli covering a wide range of 

(10) The principal organ of response is probably the eye. 

(11) The response is unsymmetrical on the part of the right and left 
sides of the animal's body. The right side is not as sensitive to stimuli 
as is the left. On the whole the right side moves through a slightly greater 
arc in a period of 45 seconds than does the left. 

(12) In the dark, other directive stimuli being eliminated, the slug 
tends to travel in a spiral of gradually increasing radius, though almost 
invariably producing one or more loops. Some slugs make right-hand 
loops, others left-hand ones ; there is a slightly greater tendency to 
right-hand circling. 

These responses of the slug to touch, gravity, and light-stimuli empha- 
size the fact that it is an animal's normal environmental conditions which 
chiefly determine its general response to artificial stimuli. The variations 
in precision and character of this general response are mainly dependent 
on certain internal factors, such as the food conditions of the animal, its 
fear of an enemy, and desire to escape captivity. 

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'97. Experimental Morphology. Part I. pp. xiv. + 280. New York. 
Davenport. C. B., and Perkins, Helen. 

'97. A Contribution to the Study of Geotaxis in the Higher Animals. Jour. 
of Physiol. Vol. 22, pp. 99-110. 


Engelmann, T. W. 

'82. Ueber Liclit- unci Farbenperception niederster Organismen. Arch. f. 
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Famintzin, A. 

'67. Die Wirkung des Lichtes und der Dunkelheit auf die Vertheilung der 
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Groom, T. T., und Loeb, J. 

'90. Der Heliotropismus der Nauplien von Balanus perforatus und die peri- 
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pp. 160-177- 
Jensen, P. 

'93. Ueber den Geotropismus niederer Organismen. Arch. f. ges. Physiol. Bd. 
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Loeb, J. 

'88. Die Orientierung der Thiere gegen die Schwerkraft der Erde (Thierischer 
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Loeb, J. 

'90. Der Heliotropismus der Thiere und seine Uebereiustimmung mit dem 
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Loeb, J. 

'93. Ueber kiinstliche Umwandlung positiv heliotropischer Thiere in uegativ 
heliotropische und umgekehrt. Arch. f. ges. Physiol. Bd. 54, 
pp. 81-107. 
Massart, J. 

'91. Recherches sur les organismes inferieurs. III. La sensibility a la gravita- 
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Peckham, G. W., and Elizabeth G. 

'98. On the Instincts and Habits of the Solitary Wasps. Wisconsin Geol. 
and Nat. Hist. Survey, Bull. No. 2 (Sci. ser., No. 1), 1898, pp. iv. 
+ 245. 14 pis. 
Fouchet, G. 

'72. De l'influence de la lumiere sur les larves de dipteres privees d'organes 
exterieurs de la vision. Rev. et Mag. de Zool., ser 2, torn. 23, 

pp. 110-117,129-138, 183-186,225-231,261-264, 312-316, pis. 12-17- 
Schwarz, F. 

'84. Der Einfluss der Schwerkraft auf die Bewegungsrichtung von Chlamido- 

monas und Euglena. Ber. deutsch. bot. Gesell. Bd. 2, Heft 2, 

pp. 51-72. 

Verworn, M. 

'89. Psycho-physiologische Protisten-studien. viii. -f- 218 pp. 6 Taf. Jena: 


"Wilson, E. B. 

'91. The Heliotropism of Hydra. Amer. Nat., Vol. 25, pp. 413-433. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 9. — November, 1901. 


By Frank Shipley Collins. 


By Frank Shipley Collins. 

Presented October 9, 1901. Received October 15, 1901. 

The earliest reference to the algae of Jamaica, and very nearly the 
earliest reference to the algae of America, appears to be by Sloane ; * in 
the chapter on submarine plants 43 species are named and described, 
among which, however, are a few aquatic phanerogams, and a considerable 
number of corals ; of the remainder most are too vaguely described to be 
now identified, but by the help of the plates, we can give with fair cer- 
tainty the modern names for four. 

Vol. I. p. 57, PI. XX. Fig. 2, Corallina opuntioides, ramidis den- 
sioribus, et Jills magls sinuatis atque corrugatis, is Halimeda Opuntia. 
P. 58, PI. XX. Fig. 3, Corallina major, nervo crassiore fuciformi, inter- 
nodla breviora nectente, White Bead Bandstring dicta, is Cymopolia bar- 
bata. P. 61, PI. XX. Fig. 9, Fucus minimus denticulalus triangularis, is 
Bryothamnion triangulare. P. 58, PI. XX. Fig. 6, Fucus marlnus vesi- 
culas habens membranis extantlbus alatas, is Turbinaria trialata. 

P. 58, PI. XX., Corallina minima capillacea, is probably our present 
Corallina capillacea, but neither plate nor description is characteristic 
enough to make this certain. P. 51, PI. XVIII. , Corallium album pumi- 
lum nostras, seems to be some species of Lithothamnion. The other de- 
scriptions are too uncertain to hazard any identifications. 

A few algae are mentioned by Browne,! apparently mostly copied from 
Sloane ; some plants undoubtedly belonging to the genus Sargassum are 
mentioned, and from the description of the great floating masses, S. 
bacciferum is undoubtedly meant, but it is probable that other species are 
included under this name. 

Lunan % gives seven species of algae, as follows, p. 157-158: 

* A voyage to the Islands Madera, Barbados, Nieves, S. Cristophers and 
Jamaica, by Hans Sloane, M.D., London, 1707. 

t The Civil and Natural History of Jamaica, by Patrick Browne, M.D., 1756. 
t Hortus Jamaicensis, by John Lunan, 1814. 


Fucus turbinatus = Turbinaria trialata. 

" natans = Sargassum bacciferum, at least in part. 
" acinarius. 
" vesiculosus. 
" triqueter. 

Ulva pavonia = Padina sp. 
" Lactuca. 

After this date, except for an occasional reference in some general 
work, we find nothing until Murray's West India list.* In this are in- 
cluded references to Sloane and Browne, and several species are added 
from specimens in the British Museum, collected by Chitty ; in a few 
cases, however, these are species so little to be expected in tropical 
regions, that it seems as if there must have been some displacement 
of labels. The total number of Jamaica species mentioned in Murray's 
list is surprisingly small, if we consider the size of the island, and that 
it has been so long a comparatively thickly settled English colony. It 
would be hardly fair to compare it with the Maze & Schramm Guade- 
loupe list, f for it is not improbable that half the species in the latter, 
certainly more than half the new species, will ultimately be relegated 
to synonymy or to the catalogue of indeterminables. As an instance 
of this, see the genus Gracilaria; 57 species are given by Maze 
and Schramm under Gracilaria and Plocaria ; 15 of these are species 
whose previously known distribution would lead one to expect them in 
Guadeloupe ; of 5, the previous record would make their occurrence here 
unlikely ; the remaining 37 are new species, with scanty description or 
none at all. Any one at all familiar with Gracilaria will recognize what 
this means. 

But as compared with Puerto Rico, for which Hauck's list t gives 92 
species against 31 Jamaica species in Murray's list, the disproportion is 
so great that it might seem as if there must be some special conditions at 
Jamaica to impoverish the marine flora. 

Within the past few years the writer has had the opportunity of ex- 
amining three collections of algae from this island, that show quite con- 
clusively that this is not the case, and that there is every reason to 

* Catalogue of the Marine Algae of the West Indian Region, by George Murray. 
Journal of Botany, Vol. XXVII. p. 224. 1889. 

t Algues de la Guadeloupe. 2d Edition. Maze & Schramm, Basse Terre, 

| Meeresalgen von Puerto-Rico, von F. Hauck. Engler's Botanische Jahrbiicher, 
Vol. IX. p. 30, 1888. 


suppose that the flora of the islaud is in no way inferior to similar 


The first collection was made by Mrs. Cora E. Pease of Maiden, Mass., 
and her sister, Miss Eloise Butler of Minneapolis, Minn. In July, 1891, 
they collected at Port Antonio and points in its vicinity ; and some 
collecting was done at other ports, where the steamer touched for a few 
hours. In 1894 Mo rant Bay was visited in July, with a visit to Borden 
and Annotto Bay the first of August, followed by Orange and Hope Bays 
and Port Antonio, where the greater part of August was spent. In 
June, 1900, short visits were made to Ora Cabessa, Rio Novo, Runaway 
Bay, and Rio Bono; June 21 to 27 was spent at Montego Bay; June 29 
to July 1 at Kingston ; and the time to July 18 was spent at Manchioueal, 
Port Morant, Hope Bay, Port Antonio, St. Ann's Bay, and Port Maria, 
in the order named. 

The second collection was made by the late Dr. J. E. Humphrey, in 
March and April, 1893, mostly at or near Kingston, but also near Port 
Antonio ; a few specimens in Dr. Humphrey's herbarium were collected 
by R. P. Bigelow at Kingston in July, 1891. In 1897 Dr. Humphrey 
made a second visit to Jamaica ; on August 16 he was attacked by the 
island fever, and died two days later. Among the collections made that 
year is a large amount of material of shell boring algae, of which he 
hoped to make a thorough study on his return ; unfortunately no one 
has been able to take up this task, and only such notes as Dr. Humphrey 
made at the time of collecting have been available for this list. 

Tlie third collection, received when this paper was practically ready 
for publication, was made near Kingston, May 3, 1901, by Dr. J. E. 
Duerden, who at that time was collecting corals for the Museum at 
Kingston. By the kindness of Dr. William Fawcett, Director of the 
Museum, arrangements were made whereby two large cans of algae pre- 
served in formalin were forwarded to the writer. Of the 47 species 
which were included, six were not represented in the other and larger 

In the following list the abbreviation P. & B. has been used for the 
first named collection, H. for the second ; where the specimens had a 
number in the Humphrey herbarium, the number is given here ; notes on 
station, depth of water, etc., have been copied; and Dr. Duerden's name 
is given for the third collection. Of one species, not included in either 
of these collections, I have received specimens from F. Borgesen, col- 
lected by O. Hansen. 

Many Jamaica algae have been distributed in the two sets of exsiccatae, 


Phycotheca Boreali-Americana, issued by Collins, Holden and Setchell, 
and Phykotheka Universalis, issued by Hauck and Richter : references 
to these are given under the respective species, with the abbreviations 
P. B.-A. and P. IL, and the numbers. 

The Humphrey collection includes 25 fresh water algae, the Pease and 
Butler collection 9 ; only two species are common to both. If we com- 
pare the marine -species * in these two collections, we find that of the 
whole number, 215, only 72 occur in both; 143 are found in one and 
not in the other. A natural inference from this would be that the field 
was by no means exhausted, and that more species might be expected. 

In Murray's list four species are given, which are omitted here : 
Gyrnuogongrus furcellatus, Phyllophora Brodiaei, Liagora viscida, and 
Plocamium coccineum, the first on the authority of Wright, the others of 
Chitty. Probably a misplacement of labels has occurred. 

Tables have been prepared, comparing the marine flora of Jamaica 
with the floras of New England, Great Britain, the northern coast of 
Spain, the coast of Morocco, the Canary Islands, aud Puerto Rico, lists 
having been published of these regions of sufficient extent to make a 
comparison of interest.! 

Some of these regions having been more thoroughly explored than 
others, too much importance should not be given to the total number of 
species in any region ; the relative proportion of the different classes is 
of more weight, while the number of species common to two regions 

* In making up these statistics, named varieties and forms have been counted 
the same as species. 

t The data of these tables are from the following works : — 

Preliminary List of New England Marine Algae, by F. S. Collins, Rhodora, Vol. 
II. p. 41, 1900. 

A Revised List of the British Marine Algae, by E. M. Holmes andE. A. L. Bat- 
ters, Annals of Botany, Vol. V. p. 63, 1892. 

Note Pre'liminaire sur les Algues Marines du Golfe de Gascogne, par C. Sauva- 
geau, Journal de Botanique, Vol. XL, 1897. 

Les Algues de P.-K.-A. Schousboe, par E. Bornet, Memoires de la Socie'te Na- 
tionale des Sciences Naturelles de Cherbourg, Vol. XXVIII. p. 165, 1892. 

Plantes Cellulaires des lies Canaries, par C Montagne, Paris, 1840. 

Crociera del Corsaro alle Isole Madera e Canarie ; Alghe, per Antonio Piccone, 
Genova, 1884. 

Contributions a la Flore Algologique des Canaries, par Mile. A. Vickers, An- 
nates des Sciences Naturelles, Series 8, Botany, Vol. IV., 1897. 

Meeresalgen von Puerto-Rico, von F. Hauck, Engler's Botanische Jahrbiicher, 
Vol. IX. p. 30, 1888. 

In addition to the published lists of the Canary Islands, some species have been 
included from the collection of the author. 


indicates the affinities of the floras. The tables are useful merely as 
showing general tendencies, not exact relations. Exactness would be 
possible only when the districts compared had been explored and studied 
to the same extent, with the same care and under the same conditions, 
a thing practically impossible. 

Table No. I. shows the distribution, in the districts named, of each 
species found in Jamaica ; Table No. II. summarizes by classes the total 
number of species for each of the seven regions, — it represents less the 
probable richness of each region, than the extent to which it has been 
explored. A tolerable test of thoroughness of exploration is often found 
in the proportion which the Schizophyceae bear to the whole number. 
Being insignificant, usually microscopic plants, they are quite overlooked 
by the non-scientific collector. Where the knowledge of a region de- 
pends on collections made by a non-scientific collector, or by a collector 
who, however competent in other departments, is not specially an algolo- 
gist, the red algae constitute a larger, the blue-green a smaller proportion 
of the whole. 

Tbe Puerto Rico collection, and in great y>art the Canary collection, 
were made by non-algologists ; the Morocco was made by a skilled al- 
gologist, but before much was known of the lower algae, or microscopes 
perfected so that they could be suitably studied. The Biscay collection 
was the work of one man, a trained algologist, studying the plants on the 
spot; while the lists for New England and Great Britain cover the most 
thoroughly studied parts of the world, and the work of generations of 
botanists. The proportion of Schizophyceae, as shown by Table No. III., 
follows these conditions fairly well. In the New England list it is ex- 
ceptionally large, as that list included a number of species, normally 
fresh water, which were found growing with marine forms, but which 
usually would not be included in a marine flora. The totals in all parts 
of the Great Britain list are increased by the fact that in that list the 
naming of forms is carried out more fully than in any of the others ; the 
percentage, however, is but little affected by this. 

It is noticeable that in the first five floras, which might be grouped as 
warm water floras, the red algae constitute over half the whole list, while 
in the two northern they are less than half, New England, the most 
arctic in character though not in latitude, having only 37 per cent. 
Puerto Rico and Jamaica, the most southern, have the highest percentage 
of green algae, 27 and 28, respectively, they being in the region of the 
Siphonaceous plants. The Canaries have less of this element, but 
more than the region farther north. The low percentage of green algae 


iii the Biscay region is noticeable, but not easy to account for. Tbe 
high percentage of brown algae in New England and Great Britain is 
due to their northern latitude, these plants becoming increasingly preva- 
lent as we go from tbe equator to the poles ; in actual arctic waters they 
constitute the most conspicuous element of the flora. 

Table No. IV. shows the number of species common to the flora of 
Jamaica and the other floras respectively ; No. V. shows the per cent of 
each class of the Jamaica flora which is found in each of the other floras ; 
No. VI. the per cent of each of the others found in Jamaica. A thor- 
oughly explored country shows a larger per cent in No. V., a smaller per 
cent in No. VI. than a region less known, but certain general deductions 
can be made. The Puerto Rican flora is closely allied to the Jamaican, 
69 percent being common to the latter ; further exploration would proba- 
bly increase rather than reduce this. The Canaries come next, and it is 
noticeable that the percentage in Table No. V. is nearly the same in green, 
brown, and red algae. In Table VI., which is perhaps the one best show- 
ing the relationships, the common elements in the European floras grow 
regularly less as the distance increases, only 8 per cent of the flora of 
Great Britain being found in Jamaica. 

, The Schizophyceae seem to vary least in different regions, the other 
classes coming, Chlorophyceae, Rhodophyceae, Phaeophyceae, the com- 
mon per cent of the latter being surprisingly small outside of Puerto Rico 
and the Canaries. 

It is worth noting that Jamaica and the Canaries have 66 species in 
common, being 30 per cent of the former and 24 per cent of the latter; 
while New England and Great Britain, at about the same distance, have 
258 in common, being 60 per cent for the former, 35 for the latter. 
This merely illustrates the general rule that beginning almost identical, 
in the Arctic Ocean, the floras of the two shores of the Atlantic diverge 
increasingly as we go south. There are, however, a few species common 
to Jamaica and the Canaries which have not apparently been found on 
the mainland of either continent ; these probably represent an actual 
communication between the two. 

Of the 34 fresh water algae, all but 2 are found in Europe, quite in 
conformity with the rule that the fresh water algae of the two continents, 
though separated by salt water, in which they cannot exist, are much 
more alike than the marine algae, inhabiting the two shores of the 


The island of Jamaica is situated in the Caribbean Sea, between lat. 
17.40 and 18.30 N. and between long. 76.10 and 78.28 W. from Green- 
wich. The land vegetation is distinctly tropical in character, though the 
high land of the interior, and the steady sea breezes of the eastern coast, 
make the climate more comfortable than might be expected from the 
latitude. The marine flora is also of a tropical character, as is showu 
by the number of species of the Dictyotales, and of green algae of the 
Caulerpaceae, Codiaceae, Valoniaceae, and Dasycladaceae, as also by the 
absence of any representative of the Lamiuariuceae. Coral abounds all 
along the shore, and the coral reefs are often richly overgrown with 

The following notes by Mrs. Pease give an idea of the character of the 
shore and the conditions for collecting algae ; occasionally throughout the 
list that follows similar notes by Mrs. Pease on special localities or forms 
will be inserted, enclosed, like this, in quotation marks. 

" The island of Jamaica is scalloped with beautiful little bays or har- 
bors, and a description of one will apply to nearly all of them. The semi- 
circular shores of these bays, about which the little villages cluster, are 
usually low for only a very short distance back from the water ; then they 
rise abruptly into steep hills or mountains. From one to several small 
rivers empty into each of these bays; the shores are often of 'tufa,' 
a porous rock, very trying to a pedestrian, but sometimes relieved by 
little stretches of sandy beach. . . . 

" At Port Antonio, which was visited at each of our trips, the harbor 
is varied by having a small island lying at its entrance, and by a bold 
point of land running out to break the shore into two little scallops 
instead of one, one of the bays being barred by a coral reef, the other 
having a very narrow channel for the entrance of vessels. This reef was 
the best collecting ground at this place; the water was shallow for quite 
a distance, and on jagged rocky bottom, the water about waist deep, 
we found a very luxuriant growth. Caulerpa clavifera grew like little 
clusters of green grapes, in big soggy masses; there were great clumps 
of the encrusted algae, Halimedas, Amphiroas, Galaxauras, Cymopolias, 
etc. ; these continued up towards the shore, and with them upon the 
rocks were those green, warty, potato-ball-like Dictyosphaerias, Padina, 
Colpomenia sinuosa, and Anadyomene stellata. Still nearer the shore, 
the water flattened out to nothing, and the bottom was sand, like pow- 
dered shell. Corallina still grew here, but the others dropped out, and 
Caulerpa ericifolia and C. plumaris covered the bottom, as club mosses 
grow in the woods. We searched here in vain for a long time for Peni- 


cillus, and only at our last visit I noticed, in water barely deep enough 
to cover them, peculiar little mounds in the sand ; brushing off the tops 
of these revealed the Penicillus capitatus, as abundant as seedling ever- 
greens in a neglected Maine pasture lot. Not far from here, on a stone 
wall at the edge of a gentleman's garden, the ribbon Ulva, U. fasciata, 
streamed out into the water, quite filling it for a distance of about a 
meter. It grew here, on a very limited area, on each of our visits, but 
we found it nowhere else on the island. . . . 

" Morant Bay is larger, and has a comparatively long stretch of sandy 
beach, but the surf comes in so heavily that seaweeding is very difficult. 
Annotto Bay is somewhat unusual, the land for some distance from the 
sea being low and swampy, with sluggish rivers entering the sea by 
several mouths, but the sandy pebbly shores retained the usual beautiful 
curve. Montego Bay has a group of small atolls overgrown with man- 
grove trees, surrounded with shallow water. Kingston has a fine large 
harbor, enclosed by a long, narrow, sandy arm. On the outside of this, 
deep water species were often washed ashore. . . . 

" The conditions under which one must collect algae in the tropics are 
somewhat different from those for collecting in the North, where we 
have the rise and fall of the tide at intervals of a few hours, alternately 
laying bare and covering the algae on the rocks. At Jamaica many 
weeds grow on rocks so situated as to be alternately bared and covered 
by the wash of the waves at intervals of a few minutes. Many of the 
Polysiphonias, Gelidiums, Gracilarias, etc., are generally found under 
these conditions. Padina and the Galaxauras occur at these stations, 
but the finest growth of Padina that we saw was at Montego Bay, from a 
road passing over a bluff, directly on the edge of the sea^jdown into which 
one could look and see Padina growing like a field of gray morning- 
glory blossoms set upon stones in the shallow, rather quiet water. Near 
by were patches of Zonaria variegata, like red-brown morning glories. 

" Much of our collecting was done from boats, rowed by two or three 
strong, experienced boatmen. We would be rowed out to the shallow 
places overgrown with grass, the water even there being to our waists, 
then jump from the boat into the water, and fish about for seaweeds. 
We always wore bathing suits and boys' thick hip rubber boots. On the 
reefs or by the ledges the waves were often strong enough to take us off 
our feet. Then we would cling closely together, one holding on to the 
other, while the latter plunged for the seaweeds. Even then we would 
sometimes be washed away from our footing. The boatmen would be 
busy keeping the boat from the rocks, and stood ready to assist us back 


into the boat, often with great difficulty. Most of the Caulerpas were 
collected in this way, at places some distance from the shore. Even when 
the plants grew near land, often the shores were so precipitous that one to 
reach them must use a boat." 

In the list that follows, the arrangement practically follows that of Die 
Natiirlichen Pflanzenfarnilien of Engler and Prantl, but the names of 
orders, families, etc., are not given ; these are shown later in Table I., 
giving the comparison of the marine flora of Jamaica with the floras of 
other regions ; the few fresh water algae are included in their appropriate 
positious in the general list, and the fact of their being fresh water plants 
is noted by a star prefixed to the name. 

General List. 

Chroococcus turgidus (Kuetz.) Naeg. Among various fresh water 
algae, forming a scum on a small roadside brook at the base of a cliff, 
near the baths, Bath, July, 1900, P. & B. P. B.-A., No. 751. Among 
marine algae, near Kingston, Duerden. 

*Gloeocapsa quaternata (Breb.) Kuetz. Roadside, Bath, July, 1900, 
P. &B. 

Chroothece Richteriana Hansg. Among other algae, in small quantity, 
Montego Bay, P. & B. 

Xenococcus Schousboei Thuret. On Spermothamnion Gorgoneum, 
Kingston, July, 1900, P. & B. 

*Oscillatoria anguina Bory. In still water, Roaring River, near St. 
Aun's Bay, March, 1893, H. 

O. Corallinae (Kuetz.) Gomont. In a pellicle on coral rock, Port An- 
tonio, March 27, 1893, II. Among other algae, near Kingston, Duerden. 

*0. formosa Bory. In still water, Roaring River, near St. Ann's 
Bay, March, 1893; Castleton, April, 1893, II. 

*0. princeps Vauch. In mats in stream, St. Ann's Bay, March, 1893, 
H; Bath, July, 1900, P. & B. 

*0. princeps forma purpurea n. f. Trichomes and stratum a 
bright purple, otherwise like type. Forming a stratum on a roadside 
brook, near the baths, July, 19.00, P. & B. P. B.-A., No. 753. 

*0. proboscidea Gomont. In a pool by " Wag Water," and in stream 
from reservoir, Castleton, April, 1893, H. 

*0. tenuis Ag. In company with O. princeps forma purpurea, Bath, 
July, 1900, P. & B. 

*Phormidium Retzii (Ag.) Gomont. In tufts on plants, Rio Cobre, 
Bog Walk, April, 1893, H. 


Lyngbya aestuarii (Mert.) Liebm. In mats on stones, Kingston, April, 
1893, H ; Port Antonio, July, 1891, P. & B. Near Kingston, Duerden. 

L. forma violacea n. f. In company with L. ma- 
juscula, Manchioneal Bay, July, 1900, P. & B. Differing from the type 
only in color. 

L. majuscula Harv. Forming a film on marine algae, Port Antonio, 
March, 1893, H. Same locality, July, 1891, P. & B. Forming exten- 
sive tufts on muddy bottom, near the mouth of a small stream, Manchio- 
neal Bay, July, 1900, P*. & B. 

*L. putalis Mont. Morant Bay, July, 1900, P. & B. 

*L. versicolor (Wartm.) Gomont. Marine Garden, Kingston, II. 
P. B.-A., No. 54. 

Symploca hydnoides Kuetz. var genuina Gomont. On rocks in shallow 
water, in small patches, not abundant, Montego Bay and Manchioneal 
Bay, 1900, P. & B. 

S. hydnoides var. fasciculata (Kuetz.) Gomont. With var. genuina, 
P. & B. 

*Plectonema Nostocorum Bornet. Among Gloeocapsa quaternata, 
Bath, July, 1900, P. & B. 

*P. Wollei Farlow. Morant Bay, Aug., 1894, P. & B. Roaring 
River, H. P. B.-A., No. 55. 

*Schizothrix coriacea (Kuetz.) Gomont. In tufts on sides of lily 
tanks, Botanic Garden, Castleton, April, 1893, H. 

*S. Mexicana Gomont. On rock in " AVag Water," Castleton, April, 
1893, No. 399, H. 

Microcoleus chtbonoplastes (Fl. Dan.) Thuret. In turfs of algae, St. 
Ann's Bay, March, 1893, H. 

M. tenerrimus Gomont. In company with M. chthonoplastes, March, 
1893, H. 

*M. vaginatus (Vaucb.) Gomont. On moist rock, Rio Cobre, Bog 
Walk, April, 1893, II. 

*Nostoc commune Vauch. In crusts on sandy soil, Constant Spring, 
April, 1893, No. 365, H. 

*N. microscopicum Carm. On steps into reservoir, Constant Spring, 
April, 1893, No. 361, H. The specimens are sterile, so that the deter- 
mination is somewhat in doubt. 

*N. verrucosum Vauch. On rocks in "Wag Water," Castleton, April, 
1893, H. No. 362, H., from trough in running water, Castleton, April, 
1893, is probably the same species. 

*Cylindrospermum muscicola Kuetz. On sides of basin, Constant 


Spring; on sand at edge of river, Castleton, April, 1893, No. 
364, H. 

Hormothamnion enteroraorphoides Grunow. In shallow water, St. 
Ann's Bay ; on coral reef, Navy Island, July 25, 1897, H. P. B.-A., 
No. 56. Near Kingston, Duerden. 

*Scytonema Arcangelii Born. & Flah. On moist rocks by spring, 
Castleton, April, 1893, H. 

S. conchophilum Humphrey ms. In old conch shell, Port Antouio, 
March, 1893, H. Kingston, June, 1897,11; Producing slight, gray, 
pustular roughenings of outside of shell, Mastigocoleus testarum occur- 
ring on inside of same shell. 

Filaments 5-8 /x diam., irregularly branched, branches single or gemi- 
nate, tips rounded, cells two thirds to two times as long as broad, 2.7- 
4.5 fx diam., pale bluish when separate. Heterocysts globose or slightly 
elongated, 5 /x diam., rarely two or three together, intercalary. Sheath 
rather thin, deep yellow, homogeneous ; when old, rough outside, hyaline 
and thin at growing tips. J. E. Humphrey. 

*S. crispum (Ag.) Bornet. On sides of trough, Constant Spring; in 
basin, Kingston, April, 1893, H. P. B.-A., No. 60. 

*S. densum (A. Br.) Bornet. In turfs, moist places, Port Antonio, 
April, 1893, H. 

*S. Hofmanni Ag. On steps of Court House, Port Antonio, April, 
1893, H. 

*S. Javanicum (Kuetz.) Bornet. On flower-pot in garden, Castleton, 
April, 1893, H. 

*S. ocellatum (Dillw.) Thuret. On old palm stems, Castleton, April, 
1S93, H. 

*Hapalosiphon fontinalis (Ag.) Bornet. • On rock, " Wag Water," 
Castleton, April, 1 893, H. 

Mastigocoleus testarum Lagerh. In old shells, Kingston, 1897, H. 

Calothrix aeruginea (Kuetz.) Thuret. On Dasya arbuscula, Montego 
Bay, June, 1900, P. & B. 

C. confervicola (Roth) Ag. On various algae, Port Antonio, March, 
1893, H. 

C. Contarenii (Zan.) Born. & Flah. On wreck on beach, Port Mo- 
rant, March, 1893, H. 

*C. fusca (Kuetz.) Born. & Flah. Among Gloeocapsa quaternata, 
Bath, 1900, P. & B. 

*C. Juliana (Meneg.) Born. & Flah. On stones in stream, Roaring 
River, St. Ann's Bay, March, 1893, H. 

VOL. XXXVII. — 16 


C. pilosa Harv. On Bostrychia tenella, Port Antonio, Aug., 1894, 
P. & B. 

Dichothrix penicillata Zan. On Cymopolia barbata, Port Maria, H. 
On Dictyota dichotomy P. & B. P. B.-A., No. 62. 

*Gloeotricbia natans (Hedw.) Rab. Under Nymphaea leaves, Botanic 
Garden, Castleton, April, 1893, H. 

*Spirogyra decimina (Muell.) Kuetz. Mauchioneal, July, 1900, 
P. & B. " 

The spores agree with this species, and as far as can be judged from 
dried specimens, the vegetative characters. A sterile Spirogyra from 
Bath has the same dimensions of cells, but cannot be specifically deter- 

Ulva fasciata Delile. In dense masses just below water mark, but 
only in one limited locality, Port Antonio, July, 1891, P. & B. 
P. B.-A., No. 221. Near Kingston, Duerden. 

U. Lactuca var. rigida (Ag.) Le Jobs. Port Antonio, Aug., 1894; 
Kingston, Montego Bay, June, 1900, P. & B. Near Kingston, Duerden. 

Enteromorpha erecta (Lyng.) J. Ag. Port Antonio, April, 1892, 
P. & B. 

E. flexuosa (Wulf.) J. Ag. Port Antonio, July, 1891 ; Runaway 
Bay, July, 1900; washed ashore, Mauchioneal Bay, July, 1900, P. & B. 
Near Kingston, Duerden. 

E. intestinalis (L.) Link. Port Antonio, washed ashore, July, 1894, 
P. & B. 

E. prolifera (Muell.) J. Ag. Runaway Bay, Montego Bay, Manchi- 
oneal, on stones; also in fresh water at Bath, on stones in river, 1900, 
P. & B. 

*Stigeoclonium tenue (Ag.) Rab. No. 366, H., locality not given. 

Diplochaete solitaria n. g. & sp. Frond epiphytic, consisting of 
a single cell, with thick, transparent wall, and bright green contents, 
spherical or flattened, the outline as seen from above round or slightly 
oval ; two hairs arising from each cell, usually opposite, and from points 
on the under surface quite near the edge. Cell 25-30^ diameter, 
half this diameter being occupied by the wall ; hairs 4-6/* diameter, 
slightly tapering, straight. On Laurencia obtusa, near Kingston, 

This minute plant was observed on a specimen of Laurencia, after it 
had been mounted for the herbarium, so that nothing is known as to its 
development, but it seems so distinct from any described genus of the 
Chaetophoraceae as to require a new name. 


Pringsheimia scutata Reinke. On Laurencia obtusa, near Kingston, 

*Mycoidea parasitica Cunningham. On leaves of various plants, 
Roaring River, March, 1893, Nos. 324 & 325 ; Bath, 1897, II. 
P. B.-A., No. 763. 

Chaetomorpha brachygona Harv. Port Antonio, July, 1891 ; Man- 
chioneal Bay, Rio Bono, 1900, P. & B. Forming dense mats on bottom 
of Kingston Harbor, April, 1893, No. 369, H. Near Kingston, 
Duerden. Hardly distinct from C. cannabina of Europe. 

C. clavata (Ag.) Kuetz. Washed ashore, Port Antonio, P. & B. St. 
Ann's Bay, March, 1893, No. 329, H. A rather slender form. 

C. aerea (Dillw.) Kuetz. Washed ashore, Port Antonio, Aug., 1894, 
P. &B. 

C. Linum (Fl. Dan.) Kuetz. Kingston Harbor, Aug., 1891, R. P. 
Bigelow. Mauchioneal, in company with C. brachygona, Morant Bay, 
June, 1900, P. & B. 

The plant from Morant Bay has very moniliform filaments, up to 
.4 mm. diameter, the cell wall thin, color light green, articulations one to 
two diameters ; perhaps a distinct species. 

C. Linum var. brachyarthra Kuetz. Port Antonio, July, 1891, P. & B. 

C. Melagonium (Web. & Mohr.) Kuetz. ? Growing in mud near the 
mouth of a river, Mauchioneal, July, 1900, P. & B. Quite like the 
northern form usually known as C. Picquotiana, but possibly not distinct 
from C. Linum. 

Cladophora fascicularis Kuetz. Port Antonio, July, 1891 ; Montego 
Bay, Mauchioneal, 1900, P. & B. ; Port Antonio, Feb., 1893, No. 
179, H. Generally distributed, usually growing on pebbles in mud in 
shallow water. 

C. crystallina (Roth) Kuetz. Ora Cabessa, June, 1900, P. & B. 

C. fuliginosa Kuetz. In turfs, Port Maria, No. 298, H. Morant 
Bay, Annotto Bay, etc., P. & B. Apparently common everywhere ; 
usually known as Blodgettia confervoides. 

C. Hutchinsiae (Dillw.) Kuetz. Port Antonio, July, 1891, P. & B. 

C- intertexta n. sp. Filaments 200-350^ diam., articulations one to 
three diameters, usually one and one half to two ; sparingly branched, 
branches naked or with short, usually secund ramuli ; terminal cells 
blunt, rounded. Tufts densely matted, prostrate. 

The plant forms dense masses on the bottom of pools, creeping over 
the coral sand and broken shells ; the upright branches are usually sim- 
ple, and the plant resembles an entangled mass of some coarse Chaeto- 


morpha rather than a Cladophora, but occasionally the free branches 
have a series of secund, two or three-celled ramuli, issuing one from each 
articulation. In the entangled mass more branching of this character 
will be found, also long normal branches in no definite order. The habit 
of C. intertexta is much like that of C. repens (J. Ag.) Harv., but the 
filaments are two or three times as large as in that species, and the color 
is a light green, somewhat whitish in drying, instead of the dull olive 
green of C. repens ; the latter has, moreover, a vaguely dichotomous 
branching, and articulations many times — according to Harvey, even 
twenty times — the diameter. C. herpestica (Mont.) Kuetz. has fila- 
ments of about the same size as C. intertexta, but it has long articula- 
tions, up to fifteen diameters, and irregular branching, with the upper 
branches fasciculate. 

Found along the shore near Manchioneal, July, 1900, P. & B. 
P. B.-A., No. 818. 

C. trichocoma Kuetz. Manchioneal, July, 1900, P. & B. 

Gomontia polyrhiza (Lagerh.) Born. & Flah. In old shells, coral and 
bones, Kingston, 1897, H. 

Bryopsis Harveyana J. Ag. In tufts on stones, Kingston Harbor, 
April, 1893, No. 367, H. 

B. pennata Lamour. In tufts on rocks, Apostles' Battery, Kingston 
Harbor, April, 1893; Port Maria, March, 1893, No. 297, H. A single 
specimen, Port Morant, July, 1900, P. & B. 

Caulerpa cupressoides var. typica Weber. On sandy bottom, Navy 
Island, Port Antonio, March, 1893, No. 188, H. ; Port Antonio, 
P. & B. P. B.-A., No. 79. 

C. cupressoides var. Turneri Weber. Port Antonio, P. & B. 
P. B.-A., No. 765. 

C. cupressoides var. mamillosa (Mont.) Weber. Among eel-grass, at 
about one meter depth, Montego Bay, July, 1900, P. & B. Including 
forma typica and forma nuda. P. B.-A. No. 765. Near Kingston, 

C. cupressoides var. ericifolia (Turn.) Weber. Port Antonio, July, 
1891, P. & B. 

C. pinnata forma Mexicana (Sond.) Weber. Montego Bay, July, 
1900, P. &B. 

C. plumaris forma longiseta (J. Ag.) Weber. Forming dense mats in 
mud in shallow water, Port Antonio, July, 1891, P. & B. P. B.-A., 
No. 27. Near Kingston, Duerden ; very luxuraint, the erect fronds 
20 cm. hi<rh. 


C. plurnaris forma brevipes (J. Ag.) "Weber. Port Antouio, July, 
1891; Montego Bay, July, 1900, among eel-grass at about one meter 
depth, P. & B. P. B.-A., No. 766. P. U., No. 672. Near King- 
ston, Duerden. 

C. prolifera (Forsk.) Lamour. Washed ashore, not common, Port 
Morant, July, 1900, P. & B. 

C. racemosa var. clavifera (Turn.) Ag. Port Antonio; Port Morant, 
at about one meter depth, July, 1900, P. & B. In tufts on rocks, 
Kingston, April 8, 1893, No. 370, H. P. B.-A., No. 707. 

C. racemosa var. clavifera forma macrophysa (Kuetz.) Weber. On 
coral reef, Port Antonio, 1894 & 1900, P. & B. Near Kingston, 
Duerden, passing insensibly into var. clavifera. P. B.-A., No. 870. 

C. taxifolia (Vahl) Ag. Washed ashore, Port Morant, July, 1900. 
Annotto Bay, 1894, P. & B. Chitty. P. B.-A., No. 768. 

C. verticillata J. Ag. In tufts on coral rocks, Port Antonio, Feb. 27, 
1893, No. 181, II. Near Kingston, Duerden. 

C. verticillata forma charoides (Harv.) Weber. Kingston, June, 
1900, P. & B. Forming fine moss-like mats in soft mud near Man- 
grove swamp, at depth of about one meter. Near Kingston, Duerden. 

Peuicillus capitatus Lam. Port Antonio, Montego Bay, Manchioneal, 
nearly buried in coral sand, 1900, P. & B. Port Maria, No. 294, H. 
Sloane. P. B.-A., No. 271. P. U., No. 523. Near Kingston, 

P. dumetosus (Lamour.) Decsne. Annotto Bay, washed ashore, 
Manchioneal, July, 1900, P. & B. Specimen without locality, H. 
P. B.-A., No. 769. 

" Penicillus dumetosus grew in some abundance in a pool near Man- 
chioneal. The pool was narrow, with precipitous tufa walls, which 
towards the sea closed over the pool in an arch, through which the waves 
broke heavily. The Penicillus grew among eel-grass, in muddy soil, 
covered by a coating of powdered shell and coral. With it were P. 
capitatus, Avrainvillea longicaulis, and Halimedas. The P. dumetosus 
looked like miniature groves of carefully trimmed evergreen trees, gray 
green in color." 

Rhipocephalus Phoenix (Ell. & Sol.) Kuetz. Port Morant, a single 
specimen washed ashore, July, 1900, P. & B. 

Avrainvillea longicaulis (Kuetz.) Murray & Boodle. Montego Bay, 
June, Manchioneal, July, 1900, P. & B. P. B.-A., No. 770. 

Avrainvillea nigricans Decsne. Singly in shallows, Port Maria, 
March 17, 1893, No. 270, H. Manchioneal, July, 1900, P. & B. 
P. B.-A., No. 771. 


" Avrainvillea longicaulis at Montego Bay grew imbedded in mud 
among eel-grass in shallow water, near a small island consisting of man- 
grove swamp. It was discovered by the sense of feeling as we were 
dredging in the mud among the eel-grass roots for Caulerpa. We were 
continually feeling through the thick soles of our rubber boots a sensa- 
tion as of stepping on drowned kittens. It proved to be the curious 
fleshy fronds of Avrainvillea, somewhat resembling a downy, dirty, 
swollen Udotea, often full of worms and other small animals. Avrain- 
villea grew also at Manchioneal, in an enclosed salt water pool, in eel- 
grass with Penicillus dumetosus, rooted in a clean bottom of powdered 
shells and coral ; but on the rocks bordering the pool was another species, 
A. nigricans, with short stems, and tops not so flabellate, resembling in 
shape our stemmed puff-balls." 

Udotea conglutinata (Sol.) Lamour. Closely set on bottom, Port 
Maria, March 17, 1893, No. 269, H. 

U. flabellata Lamour. On sandy bottom, Port Antonio, March 3, 
1893, No. 202 ; Port Maria, March 17, 1893, No. 268, H. On muddy 
bottom, Port Antonio, July, 1894; washed ashore, Moraut Bay, P. & B. 

Halimeda Opuntia (L.) Lamour. In dense tufts, Port Maria, March, 
1893, II. Port Antonio, July, 1891, P. & B. Near Kingston, Duerden. 
Sloane. Growing similarly to the preceding species. 

H. tridens (Ell. & Sol.) Lamour. In tufts, St. Ann's Bay, March 23, 
1893; Port Maria, March 17, 1893, II. Port Antonio, July, 1891, 
growing in shallow water, in soil composed of broken shells and coral. 
Near Kingston, Duerden. 

It is impossible to distinguish II. incrassata (Ell.) Lamour from H. 
tridens. In any considerable collection typical forms of each and a 
series of intermediate forms are to be found. 

II. Tuna (Ell. & Sol.) Lamour. In dense tufts, shallows, Port An- 
tonio, March 10, 1893, No. 235, H. 

Codium adhaerens (Cabr.) Ag. Port Antonio, Aug., 1894, P. & B. 
Specimen without locality, No. 293, H. 

C. tomentosum (Huds.) Stack. In immense tufts, Port Maria, March 
17, 1893, No. 266, H. Port Antonio, July, 1891 ; Kingston, July, 
1900, P. & B. Near Kingston, Duerden. Washed ashore in large 
quantities, nearly everywhere. P. B.-A., No. 168. 

Valonia aegagropila Ag. On rocks in shallows, Port Maria, March 
20, 1893, No. 296, H. Montego Bay, July, 1900, on rocks in shallow 
water, P. & B. P. B.-A., No. 772. 

V. ventricosa J. Ag. On rocks in shallows, Port Antonio, March 11, 


1893 ; Port Maria, March 20, 1893, No. 295, H. On rocks in shallow 
rough water, Mont ego Bay, June, 1900, P. & B. "Fronds smooth and 
transparent, as if made of thin green glass." 

V. verticillata Kuetz. On rocks in shallow water, Port Morant, 
Manchioneal, July, 1900, P. & B. 

Siphonocladus membranaceus (Ag.) Bornet. Growing in mats on 
rocks, near shore, Port Antonio, Aug., 1894 ; Runaway Bay, June, 
1900, P. & B. Near Kingston, Duerden. 

S. tropicus (Crouau) J. Ag. Washed ashore, Morant Bay, July, 
1894, P. & B. 

Dictyosphaeria favulosa (Ag.) Decsne. On rocks in shallows, Port 
Antonio, March 3, 1893, Nos. 205 & 271, H. On coral reef, Port 
Antonio, July, 1891, P. & B. P. B.-A., No. 124. 

Chamaedoris anuulata (Lam.) Mont. Washed ashore, Morant Bay, 
July, 1894, P. & B. 

Microdictyon umbilicatum (Velley) Zan. In dense tufts, Port Anto- 
nio, Feb. 27, 1893, No. 174, H. 

Anadyomene stellata (Wulf.) Ag. In tufts on rocks, Port Antonio, 
Feb. 27, 1893, H. Similar localities. Port Antonio, July, 1891; Kings- 
ton, Port Morant, July, 1900, P. & B. P. B.-A., No. 169. 

Acetabularia crenulata Lamour. Port Antonio, Annotto Bay, Au°\, 

1894 ; Rio Novo, June, 1900, P. & B. Near Kingston, Duerden. P. 
B.-A., No. 125. 

" At Annotto Bay Acetabularia and Dasycladus grew in water nearly 
to our shoulders, not very rough, on cobble stones, the two species grow- 
ing together like minute forests covering the stones." 

Dasycladus clavaeformis (Roth) Ag. In tufts on rocks, Port Maria, 
Apr. 19, 1893, No. 285, H; Annotto Bay, with the preceding species ; 
on pebbles washed ashore, St. Ann's Bay, 1900, P. & B. P. B.-A., 
No. 170. 

Botryophora occidentalis (Harv.) J. Ag. In salt pools, Palisadoes, 
Kingston Harbor, April 10, 1893, No. 386, H. Port Antonio, Aug., 
1894, P. & B. 

Neomeris dumetosa Lamour. Kingston Harbor, on mangrove roots, 
July, 1900, P. & B. "Looking like small green worms." 

Cymopolia barbata (L.) Lamour. In tufts on stones, St. Ann's Bay 
and Port Maria, March. 1893, H. On coral reef. Port Antonio, Annotto 
Bay, 1891 & 1894, washed ashore; Kingston, Port Morant, 1900, P. & 
B. Near Kingston, Duerden. P. B.-A., No. 28. P. U., No. 674. 


Maii} r specimens agree with the description of C. Mexicana J. Ag., but 
all intermediate forms occur, and often the same individual will agree with 
one species in one part of the frond, with the other in other parts. 

E. Mitchellae Harv. ? Kingston, March, 1893, Nos. 141, 142, 372, 
H. Not exactly like the type of this species, the plurilocular sporangia 
being longer and sometimes clavate. Possibly E. Duchassaingianus 

Striaria attenuata (Ag.) Grev. Montego Bay, June, 1900, washed 
ashore on sandy beach, P. & B. 

S. attenuata var. ramosissima (Kuetz.) Hauck. With the type, June, 
1900, P. & B. 

Colpomenia sinuosa (Roth) Derb. & Sol. On coral rocks, Port Anto- 
nio, March 8 and 23, 1893, Nos. 153 and 212; Port Maria, March 17, 
1893, No. 273, H. Annotto Bay to Port Antonio, in shallow water, 
Aug., 1894, P. & B. 

Hydroclathrus cancellatus Bory. On coral rocks, Port Antonio, Feb. 
10, 1893, No. 234, H. 

Cutleria sp. A single specimen, attached to a frond of Udotea flabel- 
lata, seems to be the Aglaozouia form of some Cutleria, but in the absence 
of fruit it is indeterminable. The frond consists of radiating articulate 
filaments, united laterally, and varying much in diameter. 

Turbinaria trialata Kuetz. Washed ashore, Port Antonio, March 8, 
1893, No. 211 ; in tide pools, Port Maria, March 16, 1893, No. 249, H. 
Washed ashore, Port Antonio, July, 1891; Montego Bay, July, 1900, 
P. & B. P. B.-A., No. 774. T. vulgare, Sloane, is undoubtedly this 

Sargassum bacciferum (Turn.) Ag. Washed ashore, Port Maria, 
March 18, No. 248, H. Sloane, Chitty. 

S. lendigerum (L.) Kuetz. Washed ashore, Port Antonio, July, 
1891, P. & B. In tufts in tide pools, Port Maria, March 17, 1893, No. 
292, H. 

S. platycarpum Mont. Washed ashore, Port Antonio, July, 1891, P. 
& B. Same locality, March 8, 1893, No. 210, H. P. B.-A., No. 775. 

S. vulgare Ag. Washed ashore, Port Maria, March 18, 1893, No. 
247, H. The references to Sloane and Chitty are doubtful, and some 
other form may have been referred to under this name. 

S. vulgare forma ovata n. f. Washed ashore, Montego Bay, June, 
1900, P. & B. P. B.-A., No. 776. Leaves thick, dark, ovate to subor- 
biculate, coarsely and sharply, sometimes doubly toothed, usually slightly 
oblique at the base. The branching is dense, the leaves numerous and 


of form and thickness mentioned above ; otherwise it agrees with typical 
S. vulgare. 

S. vulgare var. foliosissimum (Lamour.) J. Ag. Washed ashore, Port 
Antonio, July, 1891, P. & B. 

Spatoglossum Schroederi (Mert.) J. Ag. Two specimens only, washed 
ashore on sandy beach with high surf, near lighthouse, Kingston harbor, 
July, 1900, P. & B. Chitty. 

Stypopodium lobatum (Ag.) Kuetz. Washed ashore, Port Maria, 
March 10 and 19, Nos. 231 and 286; St. Ann's Bay, March 23, 1893, 
No. 311, II. Annotto Bay, July, 1891 ; Montego Bay, June, 1900, P. 
& B. P. B.-A., No. 777. 

"Stypopodium lobatum grew in magnificent clumps of two sorts, one 
with the frond narrowly divided and heavily marked with dark bars, mak- 
ing the plant resemble bunches of turkey feathers ; the other with fronds 
of broader divisions and not so prominently barred. The first mentioned 
form grew deeper down in the water, so deep as to have to be pulled off 
by the boatmen by means of a long handled boat-hook. The two forms 
were plainly distinguished as they grew in the water." 

Gymnosorus variegatus (Lamour.) J. Ag. Kingston, Montego Bay, 
1900, P. & B. P. B.-A., No. 778. 

" Gymnosorus variegatus grew with Padina, which it resembled in 
manner of growth, being in shape like clusters of short-stemmed morning 
glory flowers. It formed a covering to the rocks nearer shore than the 
Stypopodium, the water being about knee deep. G. variegatus is reddish 
brown in color, Padina gray, Sargassum and Turbinaria rich yellow 
brown ; Dictyota a darker brown with less yellow ; Stypopodium gen- 
erally grayish brown with dark markings. The contrasting colors were 
very rich in the water." 

Padina Durvillaei Bory. On rocks, Port Antonio, Feb. 28, 1893, No. 
173, H. Port Antonio, July, 1891 ; Ora Cabessa, Montego Bay, 1900, 
P. & B. Near Kingston, Duerden. The P. Pavonia of Murray and 
earlier lists is probably this species. 

Dictyopteris delicatula Lamour. In tufts on rocks, Port Maria, March 
19, 1893, II. Washed ashore, Annotto Bay, Aug., 1894; Hope Bay, 
Kingston, 1900, P. & B. P. B.-A., No. 485. 

D. Justii Lamour. Washed ashore, Port Antonio, July, 1891 ; Morant 
Bay, Annotto Bay, Aug., 1894; Kingston, 1900, P. & B. In tufts on 
rocks, Port Maria, March 17, 1893, No. 264, H. Chitty. 

D. plagiogramma Mont. Annotto Bay, July, 1894, washed ashore, 
P. & B. Chitty. 


Dictyota Bartayresiana Larnour. Washed ashore in mats, Port Anto- 
nio, March, 1893, Nos. 154, 194, 229, H. Port Antonio, July, 1891 ; 
on rocks in shallow water, Kingston, Montego Bay, Manchioneal, 1900, 
P. & B. Near Kingston, Duerden. P. B.-A., No. 579. Found in both 
broad and narrow forms, at nearly all the localities, often appearing like 
two distinct species. 

D. cervicornis Kuetz. "Washed ashore, Port Antonio, Aug., 1894, P. 
& B. Near Kingston, Duerden. 

D. ciliata Ag. In tufts on rocks, Port Maria, March 16, 1893, Nos. 
246 and 287; Port Antonio, March 10, 1893, No. 230, H. Washed 
ashore, Montego Bay, Ora Cabessa, Manchioneal, 1900, P. & B. P. B.-A., 
No. 779. All three kinds of fruit are represented in the specimens dis- 
tributed in the Phycotheca Boreali-Americana, the plants being collected 
at the same time. All are similarly arranged, occupying the whole of 
the fertile segments, except a narrow strip at the margin. The male 
plants are mostly old and battered, as if the antheridia were produced 
somewhat earlier in the season than the other kinds of fruit. 

"Dictyota ciliata at Montego Bay, June 23, 1900, grew on boulders 
near a precipitous rocky shore in water more than waist deep. It formed 
large round clumps. The water being very clear here, the hairs on the 
edge of the frond were so conspicuous as to easily distinguish in the water 
this form from other Dictyotas. The rocks in this locality were beauti- 
fully draped with the Dictyota, robust plants of Turbinaria in large thick 
masses, a Sargassum with rounded leaves, and Stypopodium in magnifi- 
cent clumps." 

D. dentata Lamour. Washed ashore, Port Maria, March 17, 1893, 
No. 265, H. Port Antonio, July, 1891, P. & B. On rocks in rough 
water, one meter or more deep. P. U., No. 669. Some specimens have 
the tips of the branches so finely divided as to seem ciliate. 

D. dichotoma (Huds.) Lamour. Kingston Harbor, July, 1891, R. P. 
Bigelow. On rocks, Port Antonio, July, 1891 ; Montego Bay, June, 
1900, P. & B. Chitty. 

D. divaricata Lamour. In various places, 1900, P. & B. Near Kings- 
ton, Duerden. Connected by intermediate forms with D. Bartayresiana. 

D. fasciola (Roth) Lamour. Washed ashore, Port Antonio, July, 
1891 ; Rio Novo, June, 1900, P. & B. 

Dilophus alternans J. Ag. Port Antonio, July, 1894, P. & B. 

D. Guineensis (Kuetz.) J. Ag. On flat rocks washed by the waves, 
in company with Gelidium rigidum, Montego Bay, Rio Novo, June, 1900, 
P. & B. 


Dictyerpa Jamaicensis n. g. & sp. Frond filiform, 1-3 mm. diam. 
up to 2 dm. long ; consisting of two layers of cells, an inner layer of large, 
colorless, cylindrical cells, about three diameters long, symmetrically 
arranged; an external monostromatic layer of brown rectangular cells 
from one to three diameters long, in distinct longitudinal series. Branch- 
ing di- or trichotomous, with occasional irregularly placed lateral branches, 
mostly at wide angles, each branch ending in a large, depressed-hemi 
spherical cell, by whose division the growth of the branch proceeds. 
Tufts of very fine, rust-colored or colorless confervoid rhizoidal filaments 
at irregular intervals on the frond. Fructification ? Washed ashore, 
Manchioneal, July, 1900. P. B.-A., No. 780. 

Though evidently belonging to the Dictyotaeeae, this plant differs 
from any genus of the family yet described, in having the frond terete 
throughout. Many Dictyotaeeae have prostrate rooting filaments from 
which the erect fronds arise, but in all species found in Jamaica this pros- 
trate growth is quite insignificant in comparison with the plant in ques- 
tion. It was found washed ashore in two places, in considerable quantity, 
and in no case shows any indication of fructification, or of producing 
erect flattened fronds. It may seem hazardous to give it a generic name, 
but as it is a plant of quite distinct habit, and cannot be now identified 
with any named form, it seems to require at least a provisional name. 

As washed up on the beach, it appeared like rolled and twisted strings. 
The dried plant is quite black in color, and under a hand lens shows 
closely set constrictions, probably due to the large interior cells being of 
uniform length, and terminating at the same level, as in the frond of 
Polysiphonia. These constrictions are lost when the frond is remoistened. 

Goniotrichum Humphrey! Collins. On woodwork of wreck, St. 
Ann's Bay, March 24, 1893, No. 31G, II. P. B.-A, No. 421. 

" Frond filamentous, solid, gelatinous, occasionally forking or dividing 
into several branches, the terminal portion consisting of a single series of 
cells ; the older part containing numerous cells, irregularly placed near 
the surface of the filament ; lateral branches abundant, simple, issuing 
nearly at a right angle, composed of a single series of cells." This de- 
scription is copied from the label of P. B.-A., No. 421. 

G. elegans (Chauv.) Le Jolis. Among other algae, on Laurencia 
obtusa, near Kingston, Duerden. 

Chantransia Saviana (Menegh.) Ardiss. Among other algae, on 
Laurencia obtusa, near Kingston, Duerden. 

Liagora Cheyneana Harv. Washed ashore, Port Maria, March 17, 
1893, No. 281 ; Port Antonio, March, 1893, No. 186, II. 


L. decussata Mont. Washed ashore, Hope Bay, July, 1891, and Aug., 
1894, P. & B. Very abundant in 1894. P. B.-A., No. 89. The finest 
species of the genus, with fronds in shape of a fir tree, sometimes over a 
meter in length. Apparently confined to the islands on the two sides of 
the Atlantic. 

L. elongata Zan. Hope Bay, July, 1891 ; Montego Bay, July, 1900, 
P. & B. 

L. pulverulenta Ag. Washed ashore, Manchioneal, July, 1900, P. 
& B. 

L. valida Harv. In large tufts, Port Maria, March 17, 1893, No. 
283; Port Antonio, March 10, 1893, No. 240, H. Hope Bay, Orange 
Bay, Montego Bay, 1891 and 1900, P. & B. Under No. 687, P. B.-A., 
a form was distributed as L. tenuis, which it now seems better to regard 
as L. valida. It is difficult to see how the two species can be distin- 
guished, when one has a large number of specimens. Harvey's name, 
being the older, must be maintained. 

Galaxaura cylindrica (Sol.) Decsne. Port Antonio, Morant Bay, 
Manchioneal and elsewhere, common, P. & B. Near Kingston, Duerden. 
Sloane. Chitty. P. B.-A., No. 134. 

G. lapidescens (Sol.) Lamour. In large tufts, Port Antonio, March 
10, 1893, No. 239, H. Annotto Bay, Port Antonio, July, 1891 ; Mon- 
tego Bay, on rocks, June, 1900, P. & B. Chitty. Not so common as 
other species of the genus. 

G. marginata (Ell. & Sol.) Lamour. On stones at tide-mark, Port An- 
tonio, March 10, No. 145 ; March 21, No. 241, H. Port Antonio, An- 
notto Bay, Montego Bay, Manchioneal, 1900, P. & B. Common, 
growing very densely on rocks. 

G. obtusata (Ell. & Sol.) Lamour. Port Antonio, July, 1891 ; Port 
Maria, July, 1900, P. & B., in company with other species of the genus. 

G. rugosa (Sol.) Lamour. In large tufts, Port Antonio, March, 1893, 
No. 131, H. Port Antonio, July, 1891 ; Rio Novo, Rio Bono, Montego 
Bay, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 133. 
P. U., No. 510. Sloane. Usually washed ashore on beaches. 

Wrangelia Argus Mont. Montego Bay, June, 1900, forming soft 
mats on rocks, P. & B. Specimen without locality, H. 

Gelidium coerulescens Crouan. Port Antonio, July, 1891 ; July, 
1900, P. & B. P. B.-A., No. 783. 

By the kindness of Dr. Bornet this plant has been compared with 
authentic specimens from Guadeloupe, and it is the plant referred to by 
Maze & Schramm, Algues de Guadeloupe, p. 199. Whether it is the 


plant of Kuetzing, Tab. Phyc, Vol. XVIII. PI. 56, from New Caledo- 
nia, is not certain. 

G. crinale (Turn.) J. Ag. Port Antonio, July, 1900, with G. coeru- 
lescens, P. & B. 

G. rigidum (Vahl) Ag. Port Antonio, July, 1891 ; Montego Bay, 
June, 1900, P. & B. P. B.-A., No. 784. Appears to be the form 
known as var. radicans (Bory) J. Ag. 

G. supradecompositum Kuetz. Mo rant Bay, July, 1894, P. & B. 
No. 227, no locality, H. 

The identification of this form is from a specimen from Fajardo, Puerto 
Rico, received from Hauck. If G. crinale were taken in a broad sense, 
it might include this form. 

Catenella Opuntia var. pinnata (Harv.) J. Ag. Manchioneal, July, 
1900, P. & B. Forming a thin greenish coating on small stones in shal- 
low water, on muddy bottom near the mouth of a small river. P. B.-A., 
No. 792. 

Agardhiella tenera (J. Ag.) Schmitz. Morant Bay, July, 1894; Mon- 
tego Bay, June, 1900, P. & B. 

Solieria chordalis (Ag. ) J. Ag. Washed ashore, Port Antonio, July, 
1891. P. & B. 

Eucheuma echinocarpum Aresch. Montego Bay, a few small plants, 
June, 1900, P. & B. 

Gracilaria Blodgettii Harv. Washed ashore, Montego Bay, June, 1900, 
P. & B. ; only a few specimens, some of which show a tendency to pass 
into G. confervoides. 

G. caudata J. Ag. Port Antonio, Aug., 1894, P. & B. 

G. cervicornis (Kuetz.) J. Ag. Washed ashore, Morant Bay, July, 
1894; Manchioneal, July, 1900, P. & B. Near Kingston, Duerden. 
P. B.-A., No. 787. Some of the plants are quite like Mediterranean 
specimens of G. armata. The Florida plant described as G. armata by 
Harvey in the Nereis Boreali-Americana seems to be different, and has 
not been found in Jamaica. 

G. compressa (Ag.) Grev. Annotto Bay, Aug., 1894, P. & B. 

G. confervoides (L.) Grev. On small stones, St. Ann's Bay, March 
23, 1893, No. 312, H. Washed ashore, Borden, July, 1894; Montego 
Bay, Manchioneal, 1900, P. & B. Near Kingston, Duerden. Common 
and variable. 

G. cornea J. Ag. Washed ashore, Rio Bono, June, 1900, P. & B. 

G. Curtissiae J. Ag. Washed ashore, Annotto Bay, Aug., 1894, 
P. & B. 


G. damaecornis J. Ag. Annotto Bay, Aug., 1894; Mauchioneal, 
July, 1900, P. & B. P. B.-A., No. 788. 

G. divaricata Harv. In short tufts, Navy Island, Port Antonio, March, 
1893, Nos. 155 and 228, H. Port Antonio, July, 1891 ; Port Morant, 
Kio Bono, June, 1900, P. & B. P. B.-A., No. 789. Generally dis- 
tributed but nowhere common. 

G. Domingensis Sond. Mauchioneal, June, 1900, P. & B. Found 
only in a very limited station, in large tufts on rocks about one meter 
depth, in rough water; very luxuriant plants, showing beautiful shades 
of violet. 

By J. G. Agardh this is considered as merely a form of G. multipartita 
var. polycarpa. Imperfectly developed specimens have some resemblance 
to that variety, but well developed plants are quite different; the habit 
reminds one rather of Laurencia pinnatifida. All three kinds of fruit 
were found in the Mauchioneal specimens, the cystocarps and tetraspores 
as usual in this genus, the antheridia in crypts, as described by Thuret 
for G. confervoides. The description of G. Krugiaua in Hauck's Puerto 
Rico list is quite suggestive of some of these specimens. 

G. ferox J. Ag. AVashed ashore, Morant Buy, July, 1894, P. & B. 

G. multipartita (Clem.) J. Ag. Port Antonio, July, 1891 ; Port Mo- 
rant. Montego Bay, Ora Cabessa, Mauchioneal, 1900, P. & B. No. 
380, no locality, H. Near Kingston, Duerden. Chitty. P. B.-A., 
No. 885. 

G. Wrightii (Turn.) J. Ag. Annotto Bay, Aug., 1894; Montego 
Bay, June, 1900, P. & B. A few plants only. 

The fresh frond is very stout and densely branched, and not at all 
compressed ; it shrinks much in drying, and herbarium specimens give 
the idea of a flattened frond. 

Hypuea divaricata Grev. In large tufts on rocks in shallow water, 
Montego Bay, Manchioneal, 1900, P. & B. 

H. musciformis (Wulf.) Lamour. On stones at tide mark, Port An- 
tonio, March, 1893, Nos. 147 and 223 ; St. Ann's Bay, March 24, 1893, 
No. 320, H. Near Kingston, Duerden. Common everywhere, P. & B. 

H. Valentiae (Turn.) Mont. Annotto Bay, Aug., 1894, P. & B. 

The species is here taken in the same sense as by Hauck, Hedwigia, 
1887, Heftl, to include H. nidifica J. Ag. and H. fruticulosa Kuetz. ; 
forms corresponding to both of these occur at Annotto Bay. 

Cordylecladia irregularis Harv. Annotto Bay, Aug., 1894, P. & B. 
Near Kingston, Duerden. 


Some of the plants from each locality have tetraspores, which appear 
not to have been previously reported. They are arranged much as in C. 
erecta, except that they are at the ends of short lateral branches, instead 
of terminal on the larger branches ; the modified portions of the branches 
being ovate or subspherical rather than lanceolate. One of the Kingston 
specimens has cystocarps, which are spherical and external on the 
branches, as in other species of the genus. 

Cordylecladia Peasiae n. sp. Fronds slender, filiform, arising from 
a more or less distinct crustaceous base, dichotomously divided, with oc- 
casional scattered or secund ramuli, usually quite short. Tetraspores 
cruciate, in the somewhat swollen and darkened tips of the branches and 
ramuli, immersed in the cortical layer. Cystocarps globular, sessile 
along the main branches. Color purplish brown, changing into whitish 
or greenish ; substance rigid. 

Somewhat resembles C. erecta, which is, however, a smaller plant, 
much less branched, and having the receptacles for tetraspores larger and 
of different shape. C. conferta and C. Andersoniana have the tetra- 
spores in densely tufted special lateral branches. C. irregularis is stouter, 
with hollow steins and with oval or subspherical lateral branches for the 
tetraspores. In C. furcellata the tetraspores are borne in branches resem- 
bling the vesicles of Chrysymenia uvaria. C. heteroclada has a flat 
frond, and C. Huntii is unrecognizable from the description of Harvey. 

Manchioneal, July, 1900, P. & B. P. B.-A., No. 791. 

Chrysymenia halymeuioides Harv. Washed ashore, Morant Bay, 
July, 1894, P. & B. 

Champia parvula (Ag.) Harv. Montego Bay, Port Maria, 1900, 
P. & B. 

Caloglossa Leprieurii (Mont.) J. Ag. Among Bostrychia, just above 
water level, Port Antonio, July, 1900, P. & B. 

Asparagopsis Delilei (Ag.) Lamour. In tree-like tufts, Navy Island, 
March 10, 1893, II. 

Laurencia cervicornis Harv. Annotto Bay, Aug., 1894; washed 
ashore, Kingston, July, 1900, P. & B. 

L. implicata J. Ag. Morant Bay, July, 1900, P. & B. 

L. obtusa (Huds.) Lamour. In tufts on rocks, Kingston Harbor, 
Apr. 8, 1893, No. 376 ; no locality, No. 224, H. Port Antonio, July, 
1891; on rocks, Montego Bay, June, 1900, P. & B. Near Kingston, 
Duerden. Chitty. 

L. papillosa (Forsk.) Grev. In tufts on rocks, Kingston Harbor, Apr. 
8, 1893, II. Port Antonio, Kingston, Montego Bay. Manchioneal, Port 


Maria, P. & B. Near Kingston, Duerden. Closely covering ledges in 
rather shallow water, also washed ashore. Chitty. 

L. perforata Mont. Densely carpeting rocks in shallow water, Mon- 
tego Bay, July, 1900, P. & B. P. B.-A., No. 794. 

L. tuberculosa var. gemmifera (Harv.) J. Ag. Washed ashore, Mo- 
rant Bay, Annotto Bay, 1894 ; Ora Cabessa, July, 1900, P. & B. 

Choudria Baileyana Harv. Hope Bay, July, 1900, P. & B. No. 
336, no locality, H. 

C. dasyphylla (Woodw.) Ag. Washed ashore, Port Antonio, July, 
1891 ; Montego Bay, June, 1900, P. & B. 

C. teuuissima (Good. & Woodw.) Ag. Washed ashore, on sandy 
beach, Montego Bay, June, 1900, P. & B. 

Acanthophora Thierii Lamour. Common on rocks in Kingston Har- 
bor, Port Maria, Nos. 176, 195, 278, 377, H. Port Antonio, July, 
1891, P. & B. Near Kingston, Duerden. 

Digenea simplex (Wulf.) Ag. In tufts on rocks, Port Maria, March 
16, 1893, No. 252 ; on stones in shallows, St. Ann's Bay, March 30, 
1893, No. 334, H. Washed ashore, Orange Bay, 1894; Manchioneal, 
July, 1900, P. & B. Near Kingston, Duerden. 

Polysiphonia cuspidata J. Ag. In tufts on piles at beach, Port Maria, 
March 16, 1893, No. 251 ; on stones in shallow water, St. Ann's Bay, 
March 30, 1893, No. 335, H. Port Antonio, Aug., 1894, covering 
rocks in shallow water; Manchioneal, Port Morant, 1900, P. & B. 

P. ferulacea Suhr. In dense tufts on rocks and eel-grass, Rio Novo, 
June, 1900, P. & B. Near Kingston, Duerden, a slender, long-jointed 

P. Havanensis Mont. On mangrove roots, Port Antonio, March 8, 
1893, No. 214; on other algae, Kingston Harbor, Apr. 8, 1893, Nos. 
374b, 375, H. Washed ashore, Montego Bay, Port Antonio, 1900, 
P. & B. Near Kingston, Duerden. 

P. Havanensis var. Binneyi (Harv.) J. Ag. Port Antonio, July, 
1891, P. &B. 

P. Pecten- Veneris Harv. On other Florideae, Port Maria, March 17, 
1893, No. 276, H. 

P. secunda (Ag.) Zan. On other algae, Kingston Harbor, Apr. 8, 
1893, No. 374, H. Washed ashore, Borden, Morant Bay, 1894, 
P. & B. 

P. subulata (Duel.) J. Ag. Washed ashore, Montego Bay, June, 
1900, P. & B. 

Only two specimens collected of this species, which has not before 


been reported from America. These agree well with specimens from 
the Mediterranean. The range of this species, as previously known, lias 
been from the English Channel to Spain, the northern shore of the 
Mediterranean and the Adriatic. 

Lophosiphonia obscura (Ag.) Falk. Covering stones in shallow water, 
Manchioneal, July, 1900, P. & B. 

Bryothamnion triangulare (Gmel.) Kuetz. In great tufts in pools, 
Port Maria, March 16, 1893, Nos. 254 and 277, H. Washed ashore, 
Annotto Bay, Aug., 1894; Ora Cabessa, June, 1900, P. & B. Chitty. 
P. B.-A., No. 95. 

B. Seaforthii (Turn.) Kuetz. Washed ashore, Port Antonio, July, 
•1891 ; Kingston, July, 1900, P. & B. 

Bostrychia tenella (Vahl) J. Ag. Port Antonio, on rocks reached 
only by spray, July, 1891, and 1894 ; Manchioneal, similar locality, July, 
1900, P. & B. P. B.-A., No. 796. 

B. Mazei Crouan. In dense tufts on rock, Port Antonio, Feb. 23, 
1893, No. 158, H. 

B. Moritziana var. intermedia J. Ag. On rocks, shore of island, 
Port Antonio, Aug., 1894, P. & B. 

" The Bostrychias grew upon rocks and ledges, usually above water, 
but dashed by spray." 

Murrayella periclados (Ag.) Schmitz. On mangrove roots, Port An- 
tonio, March 8, 1893, No. 215; in dense tufts on wood, St. Ann's Bay, 
March 24, 1893, H. Manchioneal, July, 1900, P. & B. P. B.-A., 
No. 795. 

Amansia multifida Lamour. Washed ashore, Morant Bay, Annotto 
Bay, July, 1894; Rio Bono, Rio Novo, Kingston, 1900, P. & B. 
P. B.-A., No. 94. P. U., No. 708. 

Dasya arbuscula (Dillw.) Ag. Washed ashore, Montego Bay, July, 
1900, P. & B. 

D. Gibbesii Harv. Washed ashore, Port Antonio, Aug., 1894, P. & 

D. mucronata Harv. Washed ashore, Morant Bay, July, 1894, P. 

Heterosiphonia Wurdemanni (Bailey) Falk. On Gelidium rigiduni, 
No. 276, H. Annotto Bay, Aug., 1894, P. & B. 

Dictyurus occidentalis J. Ag. Annotto Bay, Aug., 1894; Kingston, 
near the lighthouse, July, 1900, P. & B. Always washed ashore, never 
in large quantity, usually only a fragment here and there. P. B.-A., 
No. 797. 

VOL. XXXVII. — 17 


Halodictyon mirabile Zan. Washed ashore, St. Ann's Bay, March 30, 
1893, H. 

Spermotharanion Gorgoneum (Mont.) Bornet. On Codium tomento- 
siim. Port Antonio, Aug., 1894; Kingston, July, 1900, P. & B. Port 
Antonio, Feb. 27, 1893, No. 175 a, H. P. B.-A., No. 441. 

" Both cystocarps and polyspores have been found in Jamaica speci- 
mens ; in the former the spores have thick cell walls and are arranged 
as in Spermothamnion ; the involucre is only slightly developed. The 
polyspores are quite numerous, in an ovate or subspherical mass, occu- 
pying not more than half the diameter of the large, hyaline sporangium." 
Note from label of P. B.-A., No. 441. 

S. Turneri var. variabile J. Ag. On Bryothamnion Seaforthii, Kings-- 
ton, July, 1900, P. & B. 

Callithamnion byssoideum var. Jamaicensis Collins. In dense 
tufts on rocks, Port Antonio, Feb. 27, No. 170, H. P. B.-A., No. 443. 

" This plant has the divided cystocarps, with conical lobes, characteris- 
tic of C. byssoideum ; antheridia and tetraspores also agree ; but the 
habit is strikingly different, everything being condensed, the branches 
relatively shorter and stouter, and very densely set, the terminal ramuli 
often arranged more like C. corymbosum. It may possibly be the same 
as C. Hypneae Crouau in Maze & Schramm, Algues de Guadeloupe ; 
the name must be considered as provisional, awaiting comparison with 
authentic specimens of the latter." Note from the label of P. B.-A., 
No. 443. 

C. corymbosum (Eng. Bot.) Lyng. On Codium tomentosum, Port 
Antonio, Aug., 1894, P. & B. 

Haloplegma Duperryi Mont. Washed ashore, Morant Bay, Annotto 
Bay, Orange Bay, 1894; Kingston, July, 1900, P. & B. Only a few 
fragments at each place. 

Crouania attenuata (Bonnem.) J. Ag. On Cryptonemia crenulata, 
Morant Bay, July, 1894, P. & B. In small tufts, Navy Island, March 
10, 1893, H. 

Antithamnion Butleriae n. sp. Fronds erect, ecorticate, simple or 
with a few branches, which may be dichotomous, alternate, or occasion- 
ally opposite, diameter near base about 30//,, cells 3-6 diameters, walls 
thick. The lower portion of the frond or branch is naked; above that 
each cell bears normally a pair of ramuli, issuing at about two-thirds the 
height of the cell ; the lowest ramuli are simple, subulate, of from two to 
six cells about as long as broad; sometimes by the suppression of a 
ramulus the branching is apparently alternate ; farther up the frond these 


ramuli are compounded with similar smaller subulate ramelli, appearing 
first on the lower side of the ramulus. The upper pinnae have from 
each cell of the rachis a pair of ramelli which touch each other laterally, 
so that the pinna forms a continuous triangle. At the tips of the 
branches the cells are much shorter than those below, and the triangular 
compound pinnae are in contact, giving a linear outline to the whole. 
Color a rich rose. On Bryothamuion Seaforthii, Kingston, July, 1900, 
P. & B. 

From A. pteroton (Schousb.) Bornet it differs in the more densely 
branched pinnae, with ramelli on both sides, or on the lower only. From 
Ptilothamnion micropterum (Mont.) Bornet it differs by the absence of 
the apparent bifurcation of the pinua. Callithamnion microptilum Gru- 
now has much shorter articulations in the main branches, and less dense 
pinnules, which also are alternately more and less developed, as in some 
species of Ptilota. In the absence of fruit it is impossible to determine 
that the plant in question may not, when fruit is found, have to rather 
bear the name of Ptilothamnion Butleriae. 

Spyridia aculeata Kuetz. Washed ashore, St. Ann's Bay, March SO, 
1893, No. 337; in tufts, Port Antonio, March 10, 1893, No. 228, H. 

S. filamentosa (Wulf.) Ilarv. In dense tufts, Port Antonio, March 
10, 1893, No. 222, H. Port Morant, Kingston, Montego Bay, Man- 
chioneal, P. & B. Probably common everywhere. Chitty. 

Ceramium byssoideum Harv. Washed ashore, Port Antonio, July, 
1891, P. & B. 

C. clavulatum Ag. Port Maria, Nos. 275 and 301 ; Port Antonio, 
No. 183, H. Morant Bay, Manchioneal, Kingston, Montego Bay, P. & 
B. Common everywhere and very variable. 

C. fastigiatum Ilarv. Washed ashore, Port Antonio, July, 1891 ; Ora 
Cabessa, Rio Bono, Rio Novo, June, 1900. 

C. gracillimum Ilarv. On rocks, Apostles Battery, Kingston Harbor, 
Apr. 10, 1893. H. 

C. nitens (Ag.) J. Ag. Washed ashore, Port Antonio, July, 1891 ; 
Manchioneal, Montego Bay, 1900, P. & B. 

C. tenuissimum (Lyng.) J. Ag. On eel-grass, St. Ann's Bay. March 
24, 1893, No. 318, H. Port Antonio, July, 1891; Manchioneal, Mon- 
tego Bay, 1900, P. & B. P. B.-A., No. 798. The Montego Bay speci- 
mens are small, connecting the type with the following variety. 

C. tenuissimum var. pygmaeum (Kuetz.) Ilauck. On Laurencia 
obtusa, near Kingston, Duerden. P. B.-A., No. 890. A very small 
form, hardly visible to the naked eye, but in full tetrasporic fruit. 


Halymenia Floresia (Clem.) Ag. Washed ashore, Montego Bay, 
June, 1900, P. & B. 

Grateloupia filicina (Wulf.) Ag. Morant Bay, on rocks washed by the 
waves, but not really under water, July, 1894; Rio Bono, Rio Novo, 
July, 1900, P. & B. In tufts on wood, St. Ann's Bay, March 24, No. 
419; Kingston Harbor, Apr. 8, 1893, No. 381, H. 

"The Grateloupia gathered in 1900 was lying in coarse, black, dry, 
rigid tangle on the beach, totally unlike the Grateloupia found in 1894 
at Morant Bay, growing on a big boulder on shore washed by heavy surf. 
At the latter locality, when the water was over the plants they floated 
out like fine, greenish-brown hair; as the water receded the plants fell 
back on to the rock, covering it like a soft jelly. From the habit of the 
two forms, one would never suspect that they were the same species." 

G. dichotoma J. Ag. Near Kingston, Duerden. Fronds broader 
than usual in this species as found in the Mediterranean or at the Cana- 
ries, but otherwise the same. 

G. prolongata J. Ag. Near Kingston, Duerden. Agreeing well with 
Agardh's description, and with the form from California which passes 
under this name. 

Cryptonemia crenulata J. Ag. Morant Bay, Annotto Bay, and coast 
towards Port Antonio, washed ashore and growing on '' sea-fans," July 
and Aug., 1894; Kingston, July, 1900, P. & B. 

Cruoriella Armorica Crouan. On stones and shells, Annotto Bay, 
July, 1891, P. & B. 

Peysonnellia Dubyi Crouan. On corals, Port Maria, March 17, No. 
283 ; Port Antonio, Feb. 23, 1893, No. 161, H. 

P. rubra (Grev.) J. Ag. On rocks, Port Maria, March 19, 1893, No. 
291, H. 

Hildenbrantia Prototypus Nardo. On coral rock, Port Antonio, Feb. 
23, 1893, No. 161 ; Port Maria, March 20, 1893, No. 300, H. 

Melobesia farinosa Lamour. On Dictyota, etc., Port Antonio, July, 
1891, P. & B. On various algae, near Kingston, Duerden. 

M. Lejolisii Rosanoff. On various algae and eel-grass, P. & B. 

M. membranacea Lamour. On various algae, P. & B. 

M. pustulata Lamour. On Gracilaria Domingensis, P. & B. 

Lithothamniou incrustans Phil. On rocks, Port Maria, March 16, 
1893, No. 258, H. Montego Bay, July, 1900, P. & B. 

L. Lenormandi (Aresch.) Foslie. On shells, Port Antonio, P. & B. 

Amphiroa charoides, Lamour. Port Antonio, July, 1891, P. & B. 
In tufts on bottom, Port Antonio, March 2, 1893, H. 


A. debilis Kuetz. Port Antonio, July, 1891, P. & B. In tufts on 
rocks, Port Antonio, Feb. 27, No. 177 ; Kingston Harbor, Apr. 8, 1893, 
No. 382, H. Near Kingston, Duerdeu. 

A. fragilissima Laraour. Growing like a moss on coral reef and sand 
near shore, in shallow water, Port Antonio, July, 1891, P. & B. 

Murray gives this species on authority of a specimen by Sloane, but as 
he also refers to Farlow, Anderson & Eaton, No. 15, it is probable that 
Sloane's specimen is rather A. debilis. The plant distributed under No. 
15 was originally labelled A. fragilissima, but a revised label was after- 
wards issued, as A. debilis. 

Corallina capillacea Harv. Annotto Bay, Aug., 1894, P. & B. In 
dense tufts, Kingston Harbor, Apr. 8, No. 383 ; Port Maria, March 17, 
1893, H. P. B.-A., No. 150. 

C. Cubensis Mont. Annotto Bay, Aug., 1894, P. & B. In dense 
tufts, Port Maria, March 16, 1893, No. 250, H. 

C. pumila (Latnour.) Kuetz. On Turbinaria trialata, Port .Antonio, 
July, 1891 ; on Stypopodium lobatum, Montego Bay, June, 1900, P. & 
B. P. B.-A., No. 799. 

C. rubens L. In dense tufts, Port Maria, March 1G, 1893, No. 257, 
II. On rocks, Port Morant, July, 1900, P. & B. P. B.-A., No. 800. 
Sloane. Chitty. 

C. subulata Ell. & Sol. Kingston, Feb., 1896, O. Hansen. Sloane. 



Comparison of Marine Floras of Jamaica and Other Regions. 


Family Chroococcaceae. 

Chrooeoccus turgidus 

Chroothece Richteriana 

Family Chamaesiphonaceae. 
Xenococcus Schousboei 

Family Hormogoneae. 

Oscillatoria Corallinae 

Lyngbya aestuarii 

confervoides f. violacea .... 


Symploca hydnoides 

" var. fasciculata . . 
Microcoleus chthonoplastcs 


Hormothamnion enteromorphoides . . 

Scytonema conchophihini 

Mastigocoleus testarum 

Calothrix aeruginea 




Dichotlirix penicillata 


Family Ulvaceae. 

Ulva fasciata 

Lactuca var. rigida 

Enteromorpha erecta 




Family Chaetophoraceae. 
Diplochaete solitaria 

Family Mycoideaceae. 
Pringslieimia scutata 
























































TABLE I. — continued. 

Family Cladophoraceae. 

Chaetomorpha brachygona 




" var. brachyarthra .... 

Melagonium f. typica 

Cladophora crystallina 






Family Gomontiaceae. 
Gomontia polyrhiza 

Family Bryopsidaceae. 

Bryopsis Harveyana 


Family Caulerpaceae. 

Caulerpa cupressoides var. typica . . . . 
var, Turned . . . 
var. mamillosa . . 
var. ericifolia . . . 

pinnata f. Mexicana 

plumaris f. longiseta 

" f . brevipes 


racemosa var. clavifera 

f. macrophysa 

taxifolia . 


f . charoides 

Family Codiaceae. 

Penicillus capitatus 


Rbipocephalus Phoenix 

Avrainvillea longieaulis 


Udotea conglutinata 


Halimeda Opuntia 



Codium adhaerens 
































TABLE I. — continued. 

Family Valoniaceae. 

Valonia aegagropila 



Siphonocladus membranaeeus . . . . 


Dictyosphaeria favulosa 

Chamaedoris annulata 

Microdictyon umbilicatum 

Anadyomene stellata 

Family Dasycladaceae. 

Acetabularia crenulata 

Dasycladus clavaeformis 

Botryophora occidentalis 

Neomeris dumetosa 

Cymopolia barbata 


Family Ectocarpaceae. 
Ectocarpus Mitcliellae 

Family Striariaceae. 

Striaria attenuata 

" var. ramosissima . . 

Family Encoeliaceae. 

Colpomenia sinuosa 

Hydroclatbrus caiicellatus 

Family Fucaceae. 

Turbinaria trialata 

Sargassum bacciferum 




" var. foliosissimum . . . 
" f. ovata 


Family Dictyotaceae. 

Spatoglossum Schroederi 

Stypopodium lobatum 

Gymnosorus variegatus 

Padina Durvillaei 

Dictyopteris delicatula 






























TABLE I. — continued. 

Family Dictyotaceae. — continued. 

Dictyopteris plagiogramma 


Dictyota Bartayresiana 







Dilophus alternans 


Dictyerpa Jamaicensis 


Family Bangiaceae. 

Goniotriehum Ilumphreyi 


Family Helminthocladiaceae. 

Cliantransia Saviana 

Liagora Cheyneana 





Family Chaetangiaceae. 

Galaxaura cylindrica 





Family Gelidiaceae. 

Wrangelia Argus . 

Gelidium coerulescens 




Catenella Opuntia var. pinnata 

Family Rhodophyllidaceae. 

Agardhiella tonera 

Solieria chordalis 

Eucheuma echinocarpum 






































TABLE I. — continued. 

Family Sphaerococcaceae. 

Gracilaria Blodgettii 













Hypnea divaricata 



Family Rhodyrneniaceae. 

Champia parvula 

Cordylecladia irregularis 


Chrysymenia halymenioides .... 

Family Delesseriaceae. 
Caloglossa Leprieurii 

Family Bonnemaisoniaceae. 
Asparagopsis Delilei 

Family Rhodomelaceae. 

Laurencia cervicornis 





tuberculosa var gemmifera . . . 
Chondria Baileyana 



Acanthophora Thierii 

Digenia simplex 

Polysiphonia cuspidata 



" var. Binneyi .... 

Pecten- Veneris 












































































TABLE I. — continued. 

Family Rhodomelaceae. — continued. 

Polysiphonia secunda 


Lopbosiplionia obscura 

Bryothamnion Seaforthii 


Bostryehia tenella 


Moritziana var. intermedia .... 

Murrayella perielados 

Amansia multifida 

Dasya arbuscula 



Heterosiphonia Wurdemanni 

Dictyurus occidentalia 

Halodictyon mirabile 

Family Ceramiaceae. 

Spermoth amnion Gorgoneum 

Turneri var. variabile 

Callithamnion byssoideum var. Jamaicensis 


Haloplegma Dnperryi 

Crouania attenuata 

Antithamnion Butleriae 

Spyridia aculeata 


Ceramium byssoideum 






" var. pygmaeum .... 

Family Grateloupiaceae. 

Halymenia Floresia 

Grateloupia filicina , . 



Cryptonemia erenulata 

Family Squamariaceae. 

Cruoriella Armorica 

Peysonnellia Dubyi 






















































TABLE I. — continued. 

Family Corallinaceae. 

Hildenbrantia Prototypus . . . , 
Melobesia farinosa 




Lithothamnion incrustans . . . . 


Corallina capillacea 





Amphiroa charoides 
































































Summary of Marine Floras, arranged by Classes. 













Phaeopbyceae ) 
Dictyotales ) 




























Percentage by Classes in each Flora. 

























Phaeophyceae ) 
Dictyotales ) 
















Common to Jamaica in other Floras. 







Phaeophyceae ) 
Dictyotales ; 




























Percentage of Jamaica Flora common to other Floras. 







Phaeophyceae ) 
Dictyotales ) 





























Percentage of other Floras common to Jamaica. 








Phaeophyceae ) 
Dictyotales ) 

























Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. Xo. 10. — Xovembek, IDOL 



By Theodore William Richards. 



By Theodore William Richards. 

Received October 26, 1901. Presented November 13, 1901. 

The object of this paper is the description of some simple devices which 
make possible the accurate analysis of gases with a minimum of special 

I. Absorbing Pipette. 

The essential feature of Hempel's method is the use of simply con- 
structed vessels distinct from the measuring burette for the purpose of ab- 
sorbing successively the various constituents of a gaseous mixture. Hempel 
used for this end a modification of Ettling's gas pipette, which answers the 
purpose admirably ; but of course many other combinations of apparatus 
might be used. The simplest is perhaps a bulb or wide tube inserted 
over liquid contained in a bottle. In order to prevent the access of air 
into this bulb from below, it is well to make the lower part of the tube 
somewhat narrow, and to bend it upward. If desired, the capillary serv- 
ing to admit the gas may be bent downwards and then upwards, as it is 
in the Hempel pipette; but with intelligent use of the pinchcock this pre- 
caution is not necessary. A satisfactory form of the apparatus is illus- 
trated in Figure 1. 

Fifty cubic centimeters is quite enough gas for analysis, if a suitably 
narrow burette is used for measurement, hence the receiving bulb of the 
pipette (A) need not exceed seventy-five cubic centimeters in capacity. 
The bottle (C) should be capable of holding one hundred and fifty cubic 
centimetres in this case. 

The " compound pipette " of Hempel may be imitated by the addition 
at B of another bottle containing water and a levelling funnel, or the 
same object may be attained merely by connecting to the outlet B a flex 
ible rubber bulb, such as a child's toy balloon. 
vol. xxxvii. — 18 



For solids, the stem D of the pipette may be made of wider tubing, 
closed at the bottom with a perforated stopper. A small tube bent 

upwards may be inserted in this per- 
foration, if especial precaution against 
incoming air is desired. 

An explosion-pipette could be made 
of similar apparatus, with the addition 
of a stopcock just below the bulb A and 
the usual conducting wires. 

The pipette for fuming acid might be 
made with a ground-glass joint instead 
of a stopper to connect bulb with bottle. 
In that case the bottle should be pro- 
vided with a suitable side tube on the 
neck, bent upwards. 

The method of using these pipettes 
will be understood without difficulty by 
any one familiar with the Hempel 

II. Measuring Apparatus. 

The most serious cause of error in 
Hempel's ordinary apparatus is due to 
the possible change of temperature. 
This is considerably greater than the 
probable error in reading ; for a single 
degree Celsius causes an error of 0.5 
per cent of the total volume of gas 
measured under ordinary conditions, 
while the volume is easily read within 
0.05 per cent. Hence, unless much 
greater care than usual is taken to pre- 
serve constant temperature, the reading 
of the volume is unnecessarily precise. 
But Hempel's ingenious arrangements 
for maintaining constant conditions in a 100 c.c. burette are so large as 
to be inconvenient for students' use in cramped quarters. 

For these reasons I have often used somewhat smaller volumes, which 
may be surrounded with an envelope of water without producing thereby 
an unwieldy combination. An ordinary 50 c. c. burette, inverted and pro- 

Figure 1. 


vided with a levelling bulb or funnel, answers very well as a measuring 
instrument. The burette may even be used in its usual position, if it is 
provided above with a smooth rubber stopper with a single hole for the 
capillary connecting-tube. Of course the stopper is always pushed pre- 
cisely into a definite position, indicated by a carefully made mark on the 
burette. There is little risk of displacing this stopper if it is firmly wired 
into place. In any case of course the ungraduated space at the upper 
extremity must be carefully calibrated. Au especially made 50 c. c. in- 
strument, graduated all the way to the capillary tube at the top, is more 
convenient, although no more accurate than the inverted burette. For 
convenience in cleaning, it is well not to have both ends of the burette 
drawn down to small diameter. The small size of the burette makes it 
easily possible to provide the water jacket which is so essential for accu- 
rate work, and both burette and pipette may be supported upon the ordi- 
nary iron ring stand. 

III. Practical Operation. 

Of course the precautions usually necessary in gas analysis must be 
used in all the operations with this apparatus. For example, due time 
must be allowed for the running dowu 
of the liquid from the moistened walls. 
Again, care must be taken that the same Hvf 

amount of gas, at definite pressure (as 
small an amount as possible) is always 
left in the connecting capillary tubes. 
In order to make sure that no air- 
bubbles are caught, it is well to draw 
out the ends of the tubes in the manner 
illustrated in the diagram, which indi- 
cates two successive stages of the glass 
blowing, as well as the finished and con- 
nected nipple. The object of blowing 
the small bulbs is to render the bore of 
the portions drawn out as large as that 
of the rest of the tube. 

While the apparatus thus constituted 
was devised primarily for use in an emer- 
gency, it has several advantages over Figure 2. 
the Hempel apparatus. It dispenses 
with the necessity of calibrating the whole length of a new burette, it 





is very inexpensive, aud it occupies but little space. Each student may 
possess a complete set of apparatus, and every one knows the value from 
a pedagogic standpoint of such a possibility. A further advantage lies 
in the fact that the pipette is easy to fill and to clean ; and a precipitate 
in the liquid is not apt to clog its working. The short straight capillary 
brings an obvious gain of speed in transferring. Moreover, because of 
this speed, and the fact that the pressure during transference is always 
from the outside inward, the danger of loss by leakage is considerably less 
than it is with Hempel's apparatus. It is well known that in a rubber 
tube an internal pressure may cause leakage, while an external pressure 
tends to stop small outlets by causing the rubber tube to be pressed more 
closely together. 

On the other hand, the calculation is less obvious, because the volume 
taken is not just a hundred cubic centimeters ; and somewhat more care 
must be used to prevent the access of air into the pipette from below 
while shaking. A little practice enables one to shake thoroughly the 
liquid in the bulb without much agitation in the bottle if the movement is 
hinged about the point D ; hence the danger is slight. Another slight 
difficulty is the possible leakage of the absorbent around the stopper of 
the pipette bottle, — an unpleasant occurrence which has no effect upon 
the accuracy of the method. 

In presenting for general use any new instrument one must record its 
practical working in the laboratory. Everybody knows that plausible 

Analysis of known Mixtures of Air and Carbon Dioxide. 

Volume C0 2 

Volume Air 


Volume Air 



c. c. 

c. c. 

c. e. 



















37 .GO 











of positive ovt 

r negative err 

ors, 03. 


inventions do not always stand the test of indiscriminate use. Accordingly 
a large class in gas analysis has been asked to use the ne*v devices, with 
favorable outcome. 

The pipette and burette were tested as follows. A definite amount of air 
was run into the burette, and the volume measured with the usual care. 
Pure carbon dioxide was then run in from a generator, and the gain in 
volume was noted. This known mixture of air and carbon dioxide was 
run over into the new pipette, and after suitable shaking the residual air 
was returned to the burette and measured. 

These figures, taken at random from among the results of the class, 
agree with one another as well as could be expected ; and since the posi- 
tive deviation balances the negative, there is no constant error. No 
trouble was experienced as to manipulation. 

I am much indebted to Mr. Bisbee, the assistant, and to the gentlemen 
of the class in gas analysis, for their kindness in carrving out the practical 
trial of the apparatus. 

Cambridge, May 3, 1901. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 11. — January, 1902. 


By C. W. M. Black. 




By C. W. M. Black. 

Presented by W. F. Osgood. Received September 9, 1901. 


A. — Outline of Kobe's Treatment of the Problem. 

The problem of the representation, by a finite number of parametric 
formulae in two variables, of the neighborhood of a singular point of 
an algebraic surface is considered and alleged to be solved in an article 
" Sur la theorie des functions algebriques de deux variables," * by Gus- 
tav Kobb. A brief outline of Kobb's method follows : — 

1. Treatment of the Original Singular Point. 1) Let the equation 
of the surface be written in the form 

F(x,y,z) = 0, 

where F is a function of the three independent variables x, y, z analytic 
in the point x = a, y = b, x = c. The function F is transformed by 
means of a change of axes to the form 

* (6 V, = (6 V, Om + (6 V, Om+l + = (a) 

where the expression (£, 17, 'Q n is a homogeneous polynomial of degree 
n, the resulting surface (a) having the singular point considered at the 
origin, while the function (£, 77, £),„ is of a form convenient for later 

2) By the quadratic transformation 

£ = t£ , 7] = a'C, 

$ (£ rj, = tT [(r, a, 1)„, + t (r, <r, 1), )1+1 + ] ) 

= C n i<f>(T,o-) + Z X (T, (r)+ ] (b) 

* Journal de mathe'matiques pures et applique'es, 4th Series, Vol. VIII. (1892), 
p. 385. 


and the neighborhood of the original point is represented by the neigh- 
borhood of the curve 

0(t,o-)=O, f=0, (c) 

on the surface 

* (r, cr, = 0. 

3) The neighborhood of the curve (c) is included in the domains of 
a finite number of points which are 

a. regular points of the curve (c), the domain of each being repre- 
sented by a single power series 

t = V (er, I (d) 

b. critical points of the curve (c), the domain of each being repre- 
sented by an equation of the form 

t" + ^(tr, t m_1 + + /V-iO, r + ?m 0, 0=0; (e) 

c. points at an infinite distance on the curve (c), the domain of each 
being represented by an equation of form (d) or (e) in the variables 
Tj, cti, 7], where 

- = Tj , - = cr x , £<r = t; . 

cr o- 

4) The selection of the points in 3) depends upon the character of 
the curve 

(t, a) = . 

a. If c£ is irreducible, all points of class 3) b are first taken, then all 
points of class 3) c, these being regular; finally a finite number of 
points of class 3) a. Here, all the points selected, if singular, are of 
order less than m. 

h. If <f> is reducible, but contains no multiple factors, the same selec- 
tion of points holds as in a, but there may occur a singular point of 
order m. 

c. If <f> contains multiple factors, all critical points of the curves cor- 
responding to any factor, together with all points of intersection of two 
different factors, are first taken, then all points of class 3) c, these being 
possibly singular ; finally, a finite number of regular points of the several 
curves corresponding to the different factors of <£, these last points being 
possibly singular points of the surface. In this case, there may occur 
a number of singular points of order m. 

2. Treatment of Points Determined in 1. The same treatment as in 
1 is applied to each of these points and to each of the corresponding 


resulting points in turn, so long as they are singular. If after a finite 
number of such processes, all the resulting points are regular, then by 
combining the results it is assumed that the neighborhood of the origi- 
nal point is represented by the domains of a finite number of regular 
points, and so by a finite number of parametric formulae as desired. 

3. Proof that a Finite Number of the Processes of 1 will be Sufficient 
to make all Points in 2 Regular. Starting with the surface 

f(u, v, w)=0, (f ) 

in which the singular point considered is at the origin, the transfor- 
mations in 1, 1) and 2) are combined in the form 

u = (out + fro- + yOn 

v = (a 2 T + /? 2 o-+ 72 )£>- (g) 

W= (a 3 r + fi 3 o- + y 3 )0 

We can assume that 

y-2 + , y 8 4= ° 

by making, if necessary, upon / (it, r, w) a suitable homogeneous 
linear transformation. Then the next set of transformations, in 2, can 
be expressed in the form 

r=(a 1 'r 1 + /Vo-! + y/Ki ) 

<r= (a 2 ' Tl + A/o-! + y 2 ') & V (h) 

C=(o,'t 1 + /V^ + y/Kx J 

in which y 3 ' -^ 0,* and the later sets of transformations are of the same 
type with the corresponding y 3 's : 

y 3 "^0, y 3 "'t0, etc. 

So we consider a succession of transformations of type (g), which give 
a succession of surfaces with multiple points each of order m. These 
transformations will combine in the form 

«=[yiy 3 'y 3 " ys (r) + (*„ °v, £■)]£• = [A + (r r , <r r ,£ r )] {,A 

V = [y 2 y 3 'y 3 " ya" 1 + (r„ <r,, £) ] t r = [T\ + (r„ cr,, £.)] l r \ (i) 

«> = [y 3 y 3 ' y 3 " y 3 M + (r,, <r r , £.)] C = [r, + (r„ <r r , £.)] C ) 

where the symbol (t,., <r r , £ r ) represents in the expression in which it 
occurs all of the variable terms, and r 2 =}= 0, T 3 4= 0. 

* To secure this, Kobb makes unwarranted use of a quadratic transformation, 
which, however, might be replaced by a homogeneous linear transformation. He 
also overlooks one class of transformations which will arise (see 4). 


Next, as f (u, v, w) can be supposed to be irreducible, we have a 

relation of the form 

L (u, v, w)f{u, v, w) + M(u, v, w) «-[/(«, v, w)~\ — x (v, w) 


= (v, w) K + (v, w) K+ i + + (v, w) n =j= 0. (j) 

Now it is shown that the first member of equation ( j ) becomes divisible 
by £ r (m-1) (r+1) after the substitutions (i), and the establishment of an 
upper limit for the power of £ r which can then be taken out as a factor 
of the function resulting from ^ (v, w), will secure a corresponding limit 
for r, as is needed to finish the proof. 

B. — Critiqde of Kobb's Analysis. 

We now show in what respects Kobb's method and proof are at fault. 
Some of these errors are noted in a memoir " Sulla riduzione delle siuso- 
larita puntuali delle superficie algebriche dello spazio ordinario per tras- 
formazioni quadratiche," by Beppo Levi.* 

4. Kobb overlooks in his succession of transformations of type (g) 
the occurrence of transformations which arise from 1, 3), c. These are 
equivalent to 

£ = t\ v 
v = 

and here the number corresponding to y 3 ' of (h) is zero; so that the 
proof, even if correct in other respects, would fail to cover all the cases 
involved, f 

5. Without specific discussion of several unwarranted assumptions 
of Kobb.J we show by an example the failure of his proof for the 
upper limit of the exponent of the power of £,. to be taken out as a 
factor of x ( v -> w ) m (j) under the substitution (i). Let the given sur- 
face be 

f =: u 2 — 2uw — v 2 + 2vw + uvw — vw 2 — uw 2 + w z = 0. (k) 


X (v, w) = (4 + w 2 ) (w — v) 2 . 
The curve 

</> (u, v) = u 2 — 2u — v* + -2v = 

* Annali di matematica, Series 2, Vol. XXVI. (1897), p. 219. 
t Cf. Levi, 1. c, p. 224. \ Cf. Levi, 1. c, pp. 225-G. 


has a singular point at 

u = 1, V = 1. 

So the first transformation is 

i; = (o- + 1) £ V (1) 

which, applied to (k), gives 

£ 2 (r 2 - o- 2 + to-0 = (m) 


x (t.,«,)=£ 2 o- 2 (£ 2 +4). (n) 

Now the set of transformations to which Kobb is naturally led in this 
case is the following : — * 

T = Ti & O" = 0^ & £ = £j 

*"l = T 2 £ 2 0"l = 0"2 £2 £l — £2 


T = TV C, O- = OY £/> £ = £r- 

But this substitution in (11) gives 

x (v, w) = V r+2 <r* (C 2 + 4) 

in which the exponent of £ r increases indefinitely with r. 
6. In the case in which the curve 

c£ (r, «x) = 

has multiple factors, the regular points of such factors taken in 1, 4) c 
are possibly singular points of the surface, whose domains are repre- 
sented by equations of form (e). When a further quadratic transfor- 
mation is applied to such a point, we are not warranted in assuming 
that the resulting developments will represent the whole of the domain 
of the point considered. f Kobb makes this assumption in proposing to 

* This set, combined with the transformation (1), possesses all the properties 
required by Kobb in (g), (h), and (i) ; its appearance here invalidates his proof. 
It can easily be shown, moreover, that the most general set of transformations 
which he could use in this case would produce the same condition as shown here. 

t The development about the point first considered, to begin with, is a relation 
im Kleinen ; it becomes, however, on passing to the later transformations, a relation 


use in 2 only the set of points determined in 1. We are not warranted, 
either, in assuming that, when a reduction of singularity arises from the 
appearance of a term of lower degree in a different'variable from that 
with reference to which the first development is derived, the resulting 
development will hold throughout the same region as the first develop- 
ment. As an example consider the surface 

r 2 + cr£ - £ = 0. 

Regarded as a development for t, its coefficients converge for all finite 
values of o- and £ ; but when we develop for £, 

*> — , 5 

1 — O" 

and the resulting series converges only when 

| o- 1 < 1. 

7. From geometrical considerations we should not expect the quad- 
ratic transformation used to resolve the singularity in all cases. In 
ordinary space the transformation 

£ = t£, rj — cr£, 

will transform in a one-to-one manner, without change of the £ coordinate, 
all points except those in the £ = plane. Now in the surface from (m), 

t 2 - a' + t(t£ = 0, 

all points in the £-axis are singular, and whatever the reduction that 
may be secured for the origin, there will be within the neighborhood of 
the origin points whose singularity is not reduced. The same consider- 
ations would be seen to apply if we had any space curve as a singular 

Levi, in the article previously mentioned, does not attempt a proof 
of the entire proposition, but directs his work toward establishing by 
geometrical considerations the reduction of the singularity, making ex- 
ception, however, of certain cases,* which are closely related to the one 
considered in 7. 

Having thus considered the failure of Kobb to establish the proposi- 
tion even for the general case of an algebraic surface, we shall, in the 

im Grossen, the limit to the number of points taken being determined by finding 
the extent of tbe domain of each ; while the developments about the later points 
giye relations im Kleinen, as far as the first point is concerned. 

* Cf. Levi, 1. c. p. 227. Cf. also a second paper by Levi, Atti R. Ace. Sci. Torino, 
Vol. XXXIIL, 5 Dec, 1897. 


present article, supply the deficiency, and treat at once the more general 
case of an analytic surface, i. e., the case that the function F (x, y, z) is 
not merely a polynomial, but is any analytic function which vanishes 
at the point (a, b, c.) 

§ 1 
A. — The Fundamental Theorem. 

1. The theorem, the proof of which forms the subject of this article, 
is the following. 

Theorem: Let F (x, y, z) be a function such that 

1) F (x, //, z) is analytic in the three independent variables in the 
neighborhood of the point x = a, y = b, z = c ; 

2) F(a, b, c) = 0; 

3) (— \ =( 9 ~) =( — ) =0- 

\dzj[a.b,c) \5y/(a.6,c) \dzj[a,b,c) 

then we can represent all values of (x, y, z) satisfying the equation 

F(x,y, *)=0 

and lying in the neighborhood of the point (a, b, c) : 

\x — a | < S, \y — b\<8, \ z — c \<$ > 

by a finite number of parametric formulae of the following type : 
x = <f> p (u, v) 1 

y = <A P ( M > «0 y p = 1, 2, p, (A) 

z = Xp( ?/ ' v ) J 

where t/> p , if/ p , \p are analytic in the arguments (u, v) throughout a cer- 
tain region ; further for each set of values of (x, y, z), the values (0, 0, 0) 
excepted, there corresponds for at least one value of p a pair of values 
(u, v) lying within the region in which the functions <f) p , \p p , x P are con- 
sidered, and for any value of p for which this is the case, there corresponds 
no second pair of values. To the set of values (0, 0, 0) corresponds at 
least one, and in general an infinite number of pairs of values (u, v) for 
every value of p. 

2. Explanation of Symbols. The symbol (x, y, z, )„ indicates, 

in the expression in which it appears, the total collection of terms 
of degree n in the arguments taken together, which belong to that 


A functional sign expressed by means of a letter will always represent 
an analytic function. 

The symbol E (x,y, z, ) will always represent a function which 

is analytic at the point (0, 0, ) and for which E (0, 0, ) 

4= 0. If written with a subscript, as E r (x, y, z, ) it represents a 

particular function of the class; if without a subscript, it represents a 

general function of the class ; so that two functions E (z, y, z, ) 

both expressed by the same symbol, need not be equal to each other. 

B. — The Transformations. 

3. The equation 

F(x,y, z) = '0 

can be transformed to the form 

<*> (£ V, = (£ r), 0™ + (6 V, Om+i + - o 


1) m > 2, 

2) the polynomial 

(£, v , i) m = *(£, v) 

contains the term £ m , 

8) the points in which the curves corresponding to the irreducible 
factors of <£ (£, r/) cut the line at infinity shall be distinct from each 
other and from the point in which the line $ = cuts that line. 

To do this, we first make the transformation 

x = u + a, = v + b , z = w + c , 

thus obtaining 

F(x, y, z ) =f(u, v, w) = (u, v, w) m + (u, v, w) m+l + 

Here, m >; 2, the singularity now being at the origin. Next we make 
a linear homogeneous transformation with non-vanishing determinant, 

U = Ox | + /?! 7} + yi £ J 

v = a,£ + (3 2V + y,C> (1) 

w = a 3 £ + & rj + y 3 £ ) 
with the result : 

/(U, V, W) = $ ($, Tj, = (6 ">?, Dm + (£ ??> Qm+1 + = . 

For this equation, conditions 2) and 3) can be secured, as is readily seen 
by a proper choice of the coefficients in transformation (1). 


The surface $ = corresponds in the neighborhood considered, point 
for point, to the surface F = 0, and thus it is only necessary to prove 
the theorem for <t> = 0. 

We may assume that of the irreducible factors* of 4> there are none 
of degree lower than m vanishing at the point (0, 0, 0), for otherwise 
each of such factors could be treated separately by the methods here 
used, and the results combined. This provision excludes the case in 
which one of the variables has equal roots for all values of the other 
two in the neighborhood of the point (0, 0, 0). 

4. The quadratic transformation 

*=?: v = v (2) 

reduces <i> (ft r;, £) to the form 

<Kft^0 = ^W>(ft^) + £x(fti0] 

= £ m <b(lv,Q (3) 

where, au arbitrarily large positive number r having been chosen at 
pleasure, 8 can be so determined that the function <i> will be analytic 

|?|<r, \v\<t, |C|<«. 

Equation (3) follows at once from the intermediate form 

4> a, v , o = c id v, i)<» + c(#, t. iu + £ 2 (i, v, i)»+2 + ]• 

We now proceed to the proof that the function (£, 77, £) is analytic 
within the above limits. 

Let <P (ft 17, = 2 J . x . £ rf £* , t + / + * > m , 

and suppose it to be convergent when 

|f I < h, \ v \ < /,, |C| < h h> o\. 

Then, for the general term, we have 

\A ijk \^+ k <M, 

M being a positive constant. 
By transformation (2) 

<*> (ft V , = 2 j* ? 7 r i+ * 

* For the definition and the fundamental properties of the irreducihle factors 
of an analytic function of several variables, which vanishes in a point, cf. Encyclo- 
piidie der mathematischen Wissenschaften, II. B. 1, Nr. 45. 
vol. xxxvil. — 19 



*ffi* = 34* ???***- 

Now choose 8 so that r 8 < o x . 
Then, when 

|?] = r x , |^| = r 1} K| = 8, r x >i, 

the absolute value of the general term of series <fr becomes 

< | A iJk | . iy + ->' . &+j+*-" 

< | A ijk | . 8»J . S*- 

JA ljk \.W +j+k 

*> gm 

< gn, 

3 4* ??{*»**- 

Accordingly, the series 

is convergent when 

\l\<Tt |7l<Ti |C|<8,* 

and it represents an analytic function for these values of the arguments. 
5. The family of lines tangent to the surface <J> (f, ??, £) = at the 
point (0, 0, 0) forms a cone that cuts the plane £ = 1 in the curve 
$ (£, 77) = 0. If the line -q/t, = /?, £/£ = a, (a and /? being finite) is 
one of this family, then the point £ = a, -q = ft, £ = of the surface 
<1> (£, 77, £) = 0, (3) is at most a singular point of order m of that sur- 
face, and its neighborhood corresponds to a portion of the neighborhood 
of the singular point of the original surface <I> ($, rj, £) = 0. In fact, 
cut the surface 

* (6 * = 

by the plane 


Then the curve of intersection C will have a multiple point at (0, 0, 0) 
and the equations of the tangents to C at (0, 0, 0) will be 

v -j3£=0) 

> cr = 1, 2, s < m. 

* Cf. Stolz, Allgemeine Arithmetik, Vol. I. p. 293. 


Now, the transformation (2) being made, the points of the region 

T: |*| < 8, h|< 8, |C|<8, 

which lie in the neighborhoods of the lines 

> cr = 1, 2, 5, 

can, with the exception of the point (0, 0, 0), be transformed in a one- 
to-one manner on the neighborhoods of the points (0, 0, 0) of a set of 

9« (£r> VU = ° . Or = 1, 2, S , 

the coordinates being connected by the relation 

r ( 4 ) 

*=£foi + /?> S 

By the neighborhood of the above line is here meant the set of points 
(£, 7/, £) which satisfy the condition 

|*-«**|<«|C|, h-£C|:S«|C|, ICK8- 

To deal with the points for which a, /? would be infinite, cut the 

4> (£ r/, = 
by the plane 

C = o. 

The equations of the tangents to the curve of intersection at (0, 0, 0) 

f- t=1, 2, «<m. 

By means of a transformation corresponding to (2), 

the points of T which lie in the neighborhoods of the lines 

£ - « T 77 = ) 

[ T= 1, 2, < < TO, 

£ = oj 

can, with the exception of the point (0, 0, 0), be transformed in a one- 
to-one manner on the neighborhoods of the points (0, 0, 0) of the set 
of surfaces 

SV(l T ,^£) = 0, t= 1, 2, *<m, 


the coordinates being connected by the relations 

( = vi I 

By the neighborhood of the line 

£-a T r, = 0l 

is here meant the set of points (£, 77, £) which satisfy the condition 

l^-u^l^hl, |fl<«|*|, \v\<8. 

The singularities of the surfaces 

9A^ Vi, O = o, 

ff T it* v, = 

at the points (0, 0, 0) are at most of order m. Their further proper- 
ties will be considered later. 

Let G be an arbitrarily chosen (large) positive quantity, 8 a second 
suitably chosen positive quantity : then any point of T, for which 

I*i<g|ci, \v\<e\t\, o<m<s, 

is carried by the transformation (4) into one of the neighborhoods above 
considered on the surfaces g a = 0. If £ = 0, but £, 77 do not both van- 
ish, then the point (f, 71, £) is carried by (5) into one of the neighbor- 
hoods considered on the surfaces g T = 0. 

In (3), the function <j> ($, rj) contains the term $ m by 3, 2). Apply the 

V-P= *7i, (6) 

whence (3) takes the form 

* (6 v, = C" Oi (I vi) + t Xi (?» ft> 0]. 

In (j> x (£, tij), take out all terms not containing rj u so that 

_ « _ ^a _ 

01 (£ *h) = n (£ — a„) + 77 1 i^ (£, ??!), (U! + + ^ = m. 

<r = l 

Then make the transformation 

* ~ «„ = C (60 

and we have 

* (6 ,, = r tc n' & + a a - v )' v + 71 * (* a , in) + : x (k %. 0] 

<r 1 =: 1 

= Vg 9 (*„ % = (7) 


where g a has a term in ^ free from Vl aud £, since a a — a a , £ 0. So 
there are near the point (0, 0, 0) ^ values of £ a satisfying the equation 
g a — for every pair of values of ^ aud £ in the neighborhood of the 
point r\ x = 0, £ = 0. Now, for any such set of values of c , rj u £, 
different from the set (0, 0, 0), satisfying the equation g v = 0, there is 
a corresponding set of values of £, rj, £ satisfying the equation $ (f, rj, £) 
= 0, their coordinates being connected by the relations (2), (6), and (6'), 
which are equivalent to the required relation (4). Also by considering 


the other factors of IT (£ — a^ ", we get (s — 1) other equations of form 

(7), the corresponding coordinates being connected by relations of 
form (4). 

No two points (£ v , £), (£ f , v >, £') of T (distinct from (0, 0, 0)), de- 
rived from points (£ ffl rj v Q (^„ %, £2) lying respectively in the neigh- 
borhoods of the singularities which are given by two distinct equations 

9, = °, <J°' = 0, 

can be the same. For suppose 

*=& = It (4 + a,) = £ 2 U a , + a,,) 

£ = £' = Ci = £ 2 

Then we must have 

4 + a <r = £r' + <V' 

4 - £ 


and, by taking the neighborhoods of the singularities in question suffi- 
ciently small, we can insure that the difference £ v — £ a , is less in abso- 
lute value than the difference a , — a . In a similar manner it is shown 
that, if the equation g = 0, regarded as an equation in £ , has equal 
roots for all values of ij 1} £ in the neighborhood of the point -q x = 0, 
£ = 0, the equation <S> = must also have equal roots at the corre- 
sponding points, and this case has been excluded. So as each equation 
g = has near the point (0, 0, 0) p values of £ , in general distinct, 

for each pair of values of rji and £, aud as 2 /j. = m, the collection of 


g a = , o- = 1 , 2, 8 , 

has within sufficiently small limits as many different roots as the equa- 


tion 4> = 0, and thus represents the latter equation within the corre- 
sponding limits, i. e., when 

|£|<s, M<*> U< c > 


|*-a,{|<e|C| f h-i»C|<«|t|. |f|<«. 

Next we consider points for which £ = 0, but f, -q are not both zero. 
For these we use the transformation 

t = €v, t = Zy- (8) 

Then, by the same method of treatment as above, putting £ for rj and 
7) for £, and taking (3 = 0, we derive a set of surfaces 

9 v (£fV>l) = 0, t= 1, 2, <<m, 

on which are mapped all points of the original neighborhood for which 


M < 8i » i — < € i » 

I v 

and so all points for which 

Here, we have a function corresponding to <£ (J, 77) : 

<M?,f) = (|, i,1) m 

Now, for the infinite roots of 


we put the equation into the form 

( f -,.,4)=o. 

So the equation 

<M?,f) = o 

is such that its roots for £ = are the same as the ratios of the infinite 
roots of the equation 

$(lv) =o, 

and by 3, 3) these ratios are all finite. 

C. — The Number of the Neighborhoods, t u U, t, 


6. In the foregoing paragraph it has been shown that the neighbor- 
hood of each tangent line to the surface 4> = 0, at the singular point 
can be mapped on the neighborhood of a (regular or singular) point 
of the surface g = 0. We now proceed to show that the whole 


T: |*| <*, hl<S, \£\<& 

can be covered by the neighborhoods of a finite number of such lines. 
We distinguish two cases : — 

Case I. — The polynomial </> (£, 77) has no multiple factors. 
Case II. — This polynomial has multiple factors. 

Theorem: The neighborhood T can be completely covered by a finite 

number of regions T u T. 2 , T v , which overlap each other and which 

are mapped respectively on the following regions t x , f 2 , t v : 

In Case I: 1) the region t { , i = 1, 2, k, consists of the neigh- 
borhood of a singular point of the surface g w = ; 

2) the extent of each of the neighborhoods t x , t. 2 , t K having been 

arbitrarily determined^ the regions t fi j — k + 1, v, then consist 

of regular regions of surfaces g <J> = 0. 

In Case II : 1) the region t it i = 1, 2, k, consists of the neigh- 
borhood of a singular point of the surface g {i) = ; 

2) the extent of each of the neighborhoods t x , t. 2 , t K having been 

arbitrarily determined, the regions fj,j = K + 1, v, then consist 

of regions of surfaces g' j) = defined as follows ■' omitting the index j 
throughout, we write 

9 (£., Vv = [£ + ft (Vv C + + p r (Vv Ol^d,, Vv 0, 

where p e (r^, £) is analytic throughout a region 

M<h, \£\<8- 

Here r,for a given value ofj, is a positive integer satisfying the relation 
1 5; r < m. 

Case I. — The polynomial </> (f, 77) contains no multiple factors. 
Here, the equation 


can have multiple values of $ only for a finite number of values of 77, 
these being the values for which the equations 

* = 0, ^ = 

have common roots, and by the condition 3, 3) none of these values of 
r) become infinite. 

Now we consider all such values of -q 

V = c r , r = 1, 2, /, 

for which the equation, considered as an equation in J,, 

*(?,}) = <> 

has multiple roots. Deal with each of these as in 5, c r taking the place 
of /3 in (6) ; then, in equation (7), some of the // 's will, in general, be 
greater than unity, i. e. some of the equations g ■=. will have for the 
lowest terms in £ alone exponents greater than 1. For such as have 
their /x = 1, there are regular points. The others will afford singular 
points unless they have terms of the first degree in either ^ or £. 
Surround these points by neighborhoods 

141 < 8, \m\<*, |CI<*» 

i. e. 

|?-aj<&, \V-C r \ < J, \t\< 8, 

which are to be considered later. 

Now let t] = b be any value for which the equation 

<£ (?, V) = o 
has not equal roots. Then the equations g = of (7) each have a term 
in £ to the first degree, free from -q x and £, and thus the points of the 
surface g = lying in the neighborhood of the point $ a = 0, rj x = 0, 
£ = 0, can be represented by a power series 

So, in this case, we have m developments 

$,=£rO&i©i <r=l, 2, m, 

and, by using the relations (4), we have 

£=p 9 (r), Q, <r=l,2, m. 

It is readily seen that the function 

is analytic within the region 

\-m\<h-e t |C| < Sx4=0 3 

where h is the distance to the nearest value of ^ for which the equation 
corresponding to 

has a critical point, e is a positive number which can be taken arbi- 
trarily small and, having been chosen, determines an upper limit, not 
zero, for o\. In fact, f is a continuous function of the two independ- 
ent variables rj u £ within this region; furthermore, for any fixed value 
of £ such that |£| < 6 1; £ a is an analytic function of r] 1 throughout the 
region | q x \ < A — e ; and, similarly, for any fixed value of r/ x such that 
| >7i | < h ~ e ' £ is an analytic function of £ throughout the region 

Also consider the surfaces 

in 5. Here also we have m regular points of surfaces, and as a result 
m functions of the form 

These, by the same method of proof as above, are seen to be analytic 

III < *i-*, \v\ < **, 

where A is the nearest point in the 4-plane for which the equation 

has multiple roots for £, i. e. the smallest value of £ for which the 

(?, 1, ?) m = 

has equal roots for $. But this is the smallest value of - for which the 


a 1, i) 


* Cf. Briot et Bouquet's The'orie des fonctions elliptiques, § 28. The proof of 
continuity there given for polynomials in two variables will apply with very 
slight mollifications to analytic functions of any number of variables. Cf. further 
Jordan's Cours d'analyse, I. § 206, § 258. 


regarded as an equation in £/r], has equal roots. Thus — is the largest 
value of t) for which the equation 

has a critical point. So the functions are analytic and give all points 
of the original neighborhood for which 


< hi — «n \v\ < 8 2> 

or for which 

/ > jt^— = t + rrr 1 — \ = ** + «*» f*> = r)» 

thus securing the limits 

\v\ < Sai Ul < S 3 , U| > (^ + e 2 )|4l, 

where A 2 is the distance to the furthest point in the r/-plane for which the 

has a critical point, and if e 2 is first chosen arbitrarily small, 8 3 can be 
determined not zero. 

Now consider the neighborhoods of the critical points of the curve 

*(?, v) = 0. 

In these, however small we take the 8, all the remainder of a circle in 
the 77-plane including all the values for which the curve cf> = has 
critical points can be covered with circles such as were determined for 
the domains of the regular points above, these circles overlapping the 
circles about the singular points and not reaching out to these points in 
any case. Let the radius of the large circle be G where 

G > 1 , G > h, + e 2 . 

Then, if we take for 8 4 the smallest value of any ^ or S", the develop- 
ments within these circles together with the neighborhoods of the set 
of new singular poiuts will represent all points of the original neigh- 
borhood for which 

Finally, taking for 8 the smallest of the three quantities $ 2 , 8 3 , o 4 , the 


whole set of functions thus determined will represent all points of the 
original neighborhood for which 

h| < 8, |C|< 5. 

The new set of singular points may or may not be all of degrees lower 
than ?n, but if they are we have simplified the problem ; we have reduc- 
tion, as we shall say, borrowing a term frequently used in the theory 
of algebraic invariants of a linear transformation ; and if not, the further 
treatment will be considered later. 

D. — An Example. 

Before taking up Case II, however, we consider an example in which 
the degree is reduced by one quadratic transformation, and the para- 
metric representation (A) is at once secured. 

Let the surface be 

The transformation 

secures for the equation corresponding to (3) 

*(6^0 = P + ?-l-?C = O. 

(£$ = ? + ?-l 

and the critical points are 

1=0, 5=1, 

?=0, , = -l. 


and we have 


Also let 

and we have 

d = €> Vi = V ~ l t 

^ 2 + ^ 2 +2t 7i -^C=0. 

m = -i + Vti(t-&) + i- ( a ) 

£2 = l> f]i = V + ! > 

In (a) and (b), only that branch of the radical is taken which becomes 
+ 1 for zero values of the arguments. 



Again, we make the transformation 
and derive the surface 


and for the value £ = we have the roots 

? = * j I = — **• 


$3=1 — i, 
and we have the surface 

L 2 + 2*& - e - ?V& - i?V = 0, 

1 + h ^ / ?t ? 2 +4| =2 -4. 


£ 3 = 


In a similar way, from the other root, 



In (c) and (d), for the radical is taken only that branch which becomes 
+ 2 i for zero values of the arguments, and the function is seen to be 
analytic for sufficiently small values of q when 



< i - « i ; 

and similarly when 

\v\ = 

> 1 + e. 

Thus, in the ^-plane, we have 
by the formulas (a), (b), (c), (d) 
covered two, small circles about 
the points 1 and — 1 corre- 
sponding to developments (a) 
and (b), and all of the region 
outside of a circle of radius 
(1 + e), corresponding to devel- 
opments (c) and (d). We must 
now obtain further formulas 
so as to till up the remaining unshaded region. 

Consider the point 

Let £ = £ 5 — 1 and we have 

& 2 - 2 & + ?-&£+ £=0, 


^ = ^- 2 -i^-^+4. 


In the same way, about the point 

£=1, ^ = 0, 

we liave the function 


6= — + W£ 2 -4?+4 (f) 

In (e) and (f), for the radical we take only that branch which becomes 
-f 2 for zero values of the argument, and for sufficiently small values 
of f the functions are analytic when 

| rj | < 1 — e 2 . 

Agaiu, consider the point 


1 = & + 2 Vl - i , ^ = -77 + 1 + 2*, 

and we have 

^ 7 2 + 4 yi^^7 4- 7 + Vl 2 + 2 (1 + 2 1) 77 7 - £ 7 £ - 2 vT^?£ = 0, 

j^- 4 ^ 1 -*-^ 1^16-16^+^-4^-8 (l + 2^ 7 . (g) 

For the corresponding point 

4 r =-2A/l -i, ^ = l + 2», 

we have the formula 

4 Vl — * + £ 

& = 2 ^ - £ Vl6 - 16* + ? - 4 V - 8(1 + 2t) % . (h) 

In (g) and (h), for the radical we take only the branch which becomes 
+ 4 V4 — i for zero values of the arguments, the same value of the 
radical \/l — i being taken in all cases. These functions are analytic 
for sufficiently small values of £ when 

I *77 | = 1 17s | < 2 — e 7 • 
Also, considering the corresponding points of 



for which 

^ = -1 + 2*, 

V= 1-2*, 

V= -1-2/, 

we have evidently similar re- 
gions for each. Then, by taking 
the e's all small enough, we 
cover the whole unshaded re- 
mainder of the ^-plane by five 
circles within each of which there 
is a development as required. 

The sets of parametric form- 
ulae, derived by using the inter- 
mediate transformations, are 

£ = UV, 7] — v \/u (v — u) + 1 , 

£ = uv , r) = — v y/u (y — u) + 1 , 

$ = -(u 2 v + a/mV-F 4w 2 — 4), 


$ = ~(u 2 v — V«* 4 » a + 4w 2 — 4), 

7] = V, 

( = uv 




^z=^(u-V" 2 -4t; 2 +4), 

^ = -(« + V" 2 -4r 2 + 4), 

rj — uv, £ = a 
f] = uv, t, = u 






£= -( u + Vl6 — 16/ + u 2 -4v 2 -8(L + 2i)v ), 

v = u (v + 1 + 2 1) , 




M _ Vl6 - 16t + w 2 — 4u 2 - 8(1 + 2%)v ), 



with three more sets similar to (g) and (h). 

Case II. — The polynomial <£(£, rj) contains multiple factors. 

Here, any points which are common to two different irreducible 
factors of <£(£, rj), or are critical points of a single irreducible factor, 
will be critical points of the curve 

*(£v) = o, 


and all such points, a finite number in all, will be treated like the 
critical points of the previous case. But also any point on a multiple 
factor is a critical point of the curve, and further treatment is needed 
for such points. 

Suppose I = a, 7] = P is a regular point of a factor fa (£, rj) of mul- 
tiplicity r, i. e. of the irreducible factor whose rth power is equal to 
</>i(£> v) an( * not a P°i nt of an y different factor of <£(£, rj). Then, in 
the corresponding equation of form (7), g will contain a term £ r as the 
lowest term in if a free from ^ and £, and by Weierstrass's Theorem * 
we can develop the function about the point in the form 

PC + pi fa OC + + P r (*» 1 E (^ Hi = o. (9) 

These functions 

P k (vi, 0' X = l, 2, r, 

are shown by a method similar to that used for the functions in Case I 
to be analytic within a region 

hi|<A-«, KKSn 

where h is the distance to the nearest value of r/i which gives a point 
of intersection of two different irreducible curves corresponding to factors 
of <£(£, if), or to a critical point of one of the irreducible curves. 

Now none of the excepted points can be at infinity, on account of the 
provision in 3, 3). So the points on the surfaces g = in 5 will also 
afford developments of order (9), and by the method of Case I, we 
have a similar region for tbe convergence of the coefficients of the 
different powers of £ r in the polynomial, i. e. the exterior of a circle 
including all of the excepted points. 

Accordingly, in this case also, we represent the neighborhood of the 
original singular point by a finite number of neighborhoods of new 
singular points together with a finite number of functions, some of which 
are now not analytic for the values of the arguments considered, but 
satisfy equations of the form 

£ + Pl(Vl, OC + + P r (*» = - C 11 ) 

For the further treatment of these functions, we shall establish an 
auxiliary theorem in § 2. 

* See Picard's Traite d'analyse, Vol. II. p. 241. 


Any point in T'can be carried by a suitable transformation into a 
point on one of the surfaces g — or g r = 0. Let G be an arbitrarily 
chosen (large) positive quantity; then any point of T for which 

\i\< G\t\, \-n\<G\Z\, \C\<8, 

is carried by the transformation (4) into one of the neighborhoods con- 
sidered on the surfaces g = 0. 

If '(, — 0, but £ 3 77 do not both vanish, then the point (£, 77, s) is car- 
ried by (5) into one of the neighborhoods considered on the surfaces 

9 T = Q- 

§ 2. 

A. — A Lemma. 

1. The treatment of the multiple curves of Case II depends on the 

Lemma. — Given an analytic surface 

*(*» y, z ) = £(*> y) + »*(*i y> z ) — o, (a) 

<£(*, y) = 

is a multiple curve ; let <f>(x, y) have the form in the neighborhood of the 
point x = 0, y = 0, 

<f>(x,y) = [x+p(y)]'»JE(x,y), (/?) 

where p (y) is analytic at the point y = 0, and p (0) — 0. The function 
ty (x, y, z) shall be analytic at the point (0, 0, 0), but shall not be divisi- 
ble by x + p{y) at that point. Consider a region for which \y\ < h, 
and let h be chosen 

a) less than the radius of convergence of the Taylor's series which 
represents the function p (y) developed about the point y = 0, and 

b) sufficiently small, so that the points (x=p(y),y) will lie in the 
region in which E(x,y) is analytic and different from zero. Then the 
part of the neighborhood of the curve 

x + p(y)--=0, z = 0, 

which lies on the surface 

&(x,tf, z) = 

can be transformed, by means of quadratic transformations of the type 

x =■ xz, 


on a finite number of regions r u t 2 , t , which fall into two 

categories : — 

1) the region r t (i = 1, 2, k) is the neighborhood of a singular 

point of order < m ; 

2) each of the neighborhoods of 1) having been determined arbitrarily 

small, the region t s (i = k + 1 , v) is then a regular piece of an 

analytic surface, represented in its whole extent by a single set of para- 
metric formulae of the type {A). 

By the neighborhood of the curve 

x+p(y) = 0, s = 0, 

is meant the set of points (cc, y, z) satisfying the relation 

\y\<h, |*| < 8, \x + p(y)\<e. 

B. — Proof of the Lemma. 

2. To prove the lemma we begin by expressing equation (a) by means 
of (J3) in the form 

* (*, y,z) = [x+p (y)y» E(x, y) + z*(x, y, z) = 0, (y) 

and then making the transformation 

x + p (y) = x x , (S) 

thus obtaining the equation 

$0, y, z) = 4>j (a?!, y, z) = x 1 m E(x u y) + zip x (x u y, z) = 0. (y') 

Here, the function E (x u y) is analytic and different from zero in the 
neighborhood of any point x x = 0, y = y , (\y | < h), which corresponds 
to the neighborhood of the point x = p (y ), y , and lience E (x x , y) is 
analytic throughout a region including in its interior the region 

l*i I < e > \y\ < h > 

if the positive quantity € is suitably chosen. A similar remark ap- 
plies to the analytic character of the function \p x (x u y, z), and hence 
<!>! (x u y, z) is an analytic function of its three arguments throughout 
a region including in its interior the region 

l^i I < e > |y| < A » 1*1 < s - 

Now express equation (y') in the form 

*i(*n y ? z ) = 2p,..(y)^i r 2 s + F(x 1} y, z) = 0, (e) 


< r + s = mi < m, 
vol. xxxvii. — 20 



m l being the lowest degree of any term in x t and z together, and 
F(x u y, z) including all terms of degree higher than m^ in the two 
variables x u z. Each coefficient p r3 (y) may be divisible by a power 
of y, y l . In that case, however, nti must be less than m, for the term 
in x™ is present in $ a (a^, y, z). 

By means of a transformation with non-vanishing determinant, 

x x = ax x 2 -f /?! z 2 ) 

Z = a 2 X 2 + Pi Z 2 ) 

4>j can be thrown into the form : 

*i (*i> V, z ) = $2 fa, y, z 2 ) = 
9o(y)^ m t + qi(y)x 2 ' n - 1 z, + + q mi (y)z 2 "h + F,(x 2 , y, z 2 ) = (,) 

where q (y) =j= 0. 

Consider first the points of the circle \y\ < h at which q (y) = 0, if 
such exist. Each one of these points y { , (i = 1, 2, «) is a singu- 
lar point of <J> 2 = of order not greater than /«, and its neighborhood 

|*i|<«i |y-y*|<«, M< s 

may be chosen arbitrarily small. 
Surround each of these points in the 
circle \y\ = h by a circle of arbitrar- 
ily small radius e'. We now proceed 
to consider the region about an arbi- 
trary point a of the circle \y\ < h not 
lying in any of the regions just cut 
out. Let 

#2 = y — « 
and let <J>. 2 then be written in the form 

$2 (*2, y, * 2 ) = *2 (*2> Vi, * 2 ) = 

<A>0 2 )*2 mi + q~i{yd x ™ l ~ l z * + + q Mj (y-i)z, n \ -f F 2 (x 2 , y,, z 2 ) 

= [*."•« + nbtixt-i- 1 * + + r m Jy 2 )l. 2 '"qF(y 2 )+F 2 (x 2 ,y 2 ,z 2 ) 

= 0. (6) 

3. Apply to the function <I> 2 the quadratic transformation 

X 2 =^ x$ z 2 . 

* Here, for the first time, a quadratic transformation of the type that trans- 
forms but a single variable is employed. Such transformations do not occur in 
Ivobb's analysis. They appear to be indispensable. 


Let the result be written as follows : — 

<£ 2 (x 2 , y 2 , 2 2 ) = z 2 '"x<P 8 (x 3 , y 2 , z 2 ) = 

z 2 m i{[x 3 "> l + r l (i/ 2 )x z m i- 1 + + r m {y 2 )]E(y 2 ) + z 2 F & (xz,y 2 ,z 2 )} =0.(k) 

From this last equation we deduce the following theorem : — 
All points of the surface <!> = in the neighborhood of the curve 

<f>(x,y) = 0, 2i = 0, 

are mapped upon a finite number of new neighborhoods which are 

1) neighborhoods of singular points of degree < m, which neighbor- 
hoods may be taken arbitrarily small ; 

2) neighborhoods of new multiple curves on surfaces constituted like 
the surface <I> (a:, y, z) = of the lemma, the values of in thus arising 
never exceeding the original m of the lemma. 

By the same kind of reasoning as in § 1, 5, we show namely that for 
any one of the above values of a, the corresponding value of y 2 being 
in or on the circle of convergence of the Taylor's development about 
the point z 2 = of the function 

r x(V2)> A=l, 2, 


i\y2j> k — i, ±, /«!, 

all points of the surface <£ 2 = in the neighborhood of the curve 

<f>(x,y) = 0, sz = 0, 

are represented by points in the neighborhoods of points of the curve 
* 3 m ' + r x (yjx^- 1 + + r, % (y 2 ) = , z 2 = 0, 

on the surface 4> 3 = 0, i. e. if such a value of y is b, so that the corre- 
sponding value of y» is (b — a), and if the roots of the equation 

a^K + n (b - a ) x 3 m ~ l + + r mi (b - a) = (p) 

are u x , a 2 , a,„ then points of the surface 4> 2 — for which 

|*«| < 8, K| < 8, y — b, 

are connected with the points of the surface (k) by the relation 

x 2 = z, (x o + a v ) , y, — b — a, a = 1, 2, m x . 

Further, if we limit y. 2 to a circle not reaching out to the nearest point 
for which qo(y 2 ) vanishes, we have an upper limit for a„ as a root of 
the equation (u), and thus by taking z 2 and x a small enough we can make 
x 2 as small as we please. Then the transformations (8) and (£) still 


secure a limit for the values of x and 2, and thus we have represented 
a neighborhood of the curve 

<f>(x, 20 = 0, « = 0, 

on the surface 

$ (a:, y, z) = 
as required. 

Now, however small the neighborhood we shut off about the points 
in the region \y\ < h for which q (y) vanishes, since the results estab- 
lished above would hold also in a circle of radius h x > h, but still less 
than the radius of convergence of the series for p (y) in (/3), we can fill 
up the remainder of the circle of radius h with circles within which 
g (y) does not vanish, these circles overlapping at all points the bounda- 
ries of the excepted neighborhoods and not reaching up to the excepted 
points. Within each of these circles we have a development of type 
(k). Consider one of these new circles. We want to consider the 
neighborhood of the curve 

& (*» ft) = *3 m i + r x (y 2 ) x z m - 1 + + r mi (y 2 ) = 0. (v) 

If this is a multiple curve of the m x -th. order and m x < m, we have 
reduction. Moreover, if m x = m, but 

«."» + r x (y 2 )x z m ^ + + n„,(y 2 ) 4= [> a + /> 3 (y 2 )]"\, 

we also have reduction. We need consider, therefore, only the case 

*3 m ' + rx (j^W^ 1 + + r mi (y a ) = [x, + PsCya)]" 1 !, > , ,. 

m x = m, > 

and show that this case can repeat itself at most but a finite number of 

4. Suppose the function <£ 3 (x 3 , y 2 ) has the form (v'). Apply to the 
surface <J> 3 (x s , y 2 , z 2 ) = 0, (k), the transformation 

x s + p 3 (yz) = x i> 

and reduce the result to the form 

^O^ y» z*) = x^Efa) + 22-^4(^4) yt, 22) = (0). (o) 

If any term in z 2 F i (x i , y 2 , z 2 ) is of degree in x i and z 2 together less 
than m u it appears at once that we have a line of lower order. So we 
assume there are no such terms. Also, as the coefficient of a; 4 m i does 
not vanish identically in y 2 (in fact, not at all) no transformation of 


type (£) is needed, and after collecting all terms of the m r th order we 
make at once the substitution 

and proceed in the same manner as before if the degree is not reduced. 
For convenience, we suppose the succession of multiple curves of the 
same order to begin with that on the surface 4> = 0, and use a nota- 
tion independent of that hitherto employed. 
Our successive transformations are of the type 

x —pi (y) = *i 


x v - x -p v (y) = x 


x - p x (y) +p*(y)z + pz(y)z' x + + p v (y)z v ~ 1 + x/. Q>) 

Develop the function <J> in (y) by Weierstrass's Theorem : 

<P(x, y, z) = [x m + q x (y, z)x m ~ 1 + + q m (y, z)-]E(x, y, z) 

= F(x,y, z)E(x,y,z). 

From (p) we derive the relation : 

9F _9F9x v __ 1 9F 



x x z y 


x 2 z 





X z 

v J 

9x v 9x 

z v 9x v 


The succession of transformations (jr) so long as it does not reduce the 
degree in x and z, takes out of the F factor at each step the factor z v , 
since, on account of the constant term in the E factor, no power of z 
could come out of it. So, after the v transformations (ir), we have 

F(x,y,z) = z Vm F(x v ,y,z) = 

*"'"[<" + q»(2f, z)K"- 1 + + 9 mv bt, *)]. to 

and by (o-) 

9F , 9F„ 

Qx 9x v 

Now we may consider i^as having no multiple factors vanishing at the 
point (0, 0, 0). So we have the relation 

L(x,y, z)F+ M(x,y, *)^= Rfa z)=z*R l (y, z) (?) 



fi(y,z)±0, -fiifo, 0)£0. 

Substitute in equation (y) for x from (p), using for F and 7=— their 

values as derived above, and we have 

z™ L v (x v , y, z) F v + z«™-"M v (x v , y, z) ^— = z* R 1 (y, z). 


The left side of this equation is divisible by z vim ~ 1} and so the right side 

must be also. 

v(m — 1) ^ A, 

and we have an upper limit for v, the number of transformations which 
leave the order of the multiple line unchanged. 

The securing of the regions of class 2) in 1, follows from the reduc- 
tion just proved. If for all multiple curves of order n or less the lemma 
is assumed to hold, this reduction establishes it for all curves of order 
n + 1, since by it the neighborhoods are represented by those of lower 
order. But we know it to be true for curves of the first order, and so 
by mathematical induction we establish it for curves of all orders. 

5. Hie neighborhoods of singular points in 3, if they are of the m-th 
order can be taken along the curve 

<f>(x,y) = 0, z = 0, 

on the surface 

®(x,y, z) = 0. 

In fact, the first lot of points excepted, those for which in equation 
(77) q (y) vanishes, are along the line 

x 2 = , 2 2 = , 

which is connected with the original curve by the one-to-one transfor- 
mations (8) and (0- Also so long as the multiple curve does not break 
up into simpler curves, the neighborhoods correspond, and when this 
reduction takes place we can cut out the neighborhoods of the points 
common to all of the resulting curves uy cutting out neighborhoods 
along the original curve for the same values of y. 

C. — The Reduction of the Original Singularity. 

The transformations hitherto considered, when applied to the original 
surface 3> (f, rj, £) = 0, make it possible to map the neighborhood of 
the point (0, 0, 0) of that surface on a finite number of regions which 
are of two classes : — 


1) neighborhoods of singular points of transformed surfaces ; 

2) regular pieces of transformed surfaces. 

The pieces of class 2) lead at once to representation by means of para- 
metric formulae of type (A). The singular points of class 1) are all 
of lower order than the original singularity except in one case, and it 
is this case that it remains to consider in §§ 3, 4. The case can pre- 
sent itself at the outset only if the polynomial (£, rj, Q m is the product 
of m linear factors in £, rj, £, all vanishing for a single set of values of 
the arguments $, rj, £ not all zero. Geometrically, the tangent cone, 
($, rj, £)„, = 0, of the surface <J> (£, rj, £) = at the point (0, 0, 0) con- 
sists of m planes having a common line of intersection. It is found 
necessary to distinguish two sub-cases according to whether the planes 
themselves are not all coincident, or are all coincident. 

To sum up, then, we already have reduction in all cases except when 
we are led to singular points in class 1) of the particular type just 

A. — The Singular Points of Special Ttpe. 

1. In the special case in which the function (£, rj, £) m is composed of m 
linear factors, each vanishing for all points on a common line, it is possi- 
ble to reduce the singularity by means of a finite succession of quadratic 
transformations together with certain additional transformations. 

We consider two cases : — 

Case A. — The m linear factors of (|, rj, £) m are not all equal. 

Case B. — The m linear factors of (£, rj, £) m are all equal. 

2. Case A. — (£, rj, £) m is composed of m linear factors not all equal. 
The surface can be expressed in the form 

*(6 rj, = (ft rj) m + (ft rj, Q m+1 + = (13) 

where (£, 77),,, contains terms in both $" 1 and r/" 1 . 
If the surface were in a form 

f(u, v, w) — (u, v, io) m -I- (u, v, w) m+1 + = 

with the condition that the m linear factors of {u, v, w) m all vanish for 
the line 

u = aw, v = (iw, 

we could make the transformation 

^ — u — aW, rj — V — /?«>, £ = W, 



and all the resulting linear factors would have to vanish when 

£ = 0, 77 = 0, 

and so not contain £. 

Also by a linear homogeneous transformation in £ and rj we can se- 
cure the presence of terms in £"* and rf 1 , and in such case every linear 
factor of <£ (f, rj), which here is (£, rj) m itself, will contain $ and thus 
secure condition 3) of § 1, 3. 

B. — Quadratic Transformations. 

3. The succession of surfaces and corresponding quadratic transfor- 
mations which are applied to the new singular points as found, so long 
as they do not reduce the degree, can be written in the form 

^ (14) 

Apply to the surface (13) the transformation 

f = £i£i 7 = 7i£> 

and we have 

*(£, r;, o = r"[(^ >?o m + £&, ti, i) m+ i + ] 

= r[&, 7i)»K«A(^,7i» 0] as) 

= r*i(ii,7i, 0- 

As we assume the transformation does not reduce the degree of the 
singular point, there can be no term of degree less than m in the part 
^(iu 7u £) and as all terms of this contain £, when we put the expres- 
sion in the form 

*, Hi, VI, = (*1. 7l, Om + (*„ 71, 0-+1 + ( 16 ) 

we will secure reduction by another quadratic transformation unless 
($v 7i» Om is tne product of w linear factors with a common line of 
intersection. In this case the factors cannot be all equal," for then 
(£i> Vi> 0)m would have its linear factors all equal, but these are the 
factors of (£ 1} rji) m . Also the common point of intersection of the lines 


in which the plane £ = 1 cuts the planes corresponding to these factors 
is at a finite distance. We have now the conditions 2) and 3) of § 1, 3, 
and are ready to apply the transformations 


*i (&, *, = C" [(& vi, 1). + C(fi. vu i) m+ i + ] = 0. (17) 

Now if f] = y 2 , r;x = S 2 , is the common point for which the m factors of 
(li> t)u l)m vanish, then the substitution 

& = fi — y2> % = vi ~ ^2> 

gives a group of with degree terms in £ 2 an d 770 exactly corresponding to 
the terms of (£, rj) m . So in the successive collection of terms of the 
wth degree, the terms of (£, rf) m are always carried over with merely 
a change of subscript, and thus we never introduce the condition of m 
equal linear factors. Accordingly so long as the degree of the singular 
point is not reduced, the intermediate transformations are of the type 

vh = s ~~ vi-i ' vr ~ \ — <V+i * 

thus securing the succession of transformations (14). 

4. The succession of transformations in 3 will lead to the relation 

e-Z (&, * <*>, + M(U Vv ,£) tf-*» 9 ^ = B( V ,£)$0 (18) 

**(£,, >to = &*(£», Vv, l)E(Jsv, yv, 0- 
Combining transformations (14) we have the relations 

£ = yi£ + y 2 £ 2 + + y,P + P&\ 

v = s 1 z + 8 2 f+ + 8 v z» + e> Vv ] 

*(6 v, = C"**(t» n» 

As <I> contains both £ m and rj m terms, we can develop by Weierstrass's 

*(*, * = [£" + j»i(* OF'' 1 + +Pm(v,Q]Ei(e, v, 

*(6 * = Df + ?i(& 0v m ~ l + + ?„(*, 0]^(£, v, 

= * (^ 17, ^ 2 (6 V, 0- ' 

As the function i£, (£, 17, £) contains a constant term, when the first trans- 
formation of (14 y i is made, the factor £"• must come out of the <i>, and a 



similar result is true for all of the succeeding transformations. So in the 

first part of (14) we could write <l> for <£, ^ for 3> M , (^ = 1, 2, v) 

where the <i>'s are derived successively in the same way as the 3>'s. At 
each stage the $ factor must contain all the terms of lowest degree in 
the corresponding <P (except for a constant multiple), and no lower 
terms ; for, otherwise, either there would be lower terms in the product 
by the corresponding E factor on account of its constant term, or the 
required terms would not be present. 
Now, by (19), 

5* _5$ 9£y_ J_5<5> 



<i> = 

£, mv ® v ; 





, we 



_ £(m 


9<5> v 
9£ v 


But as <f> has no multiple factors vanishing at (0, 0, 0) (see § 1,3), we 
have the relation 

L($, v , 0* + M& V) || = R(v, + 0. (24) 

Then, substituting for £ and 77 from (19) on the left side of equation (24) 
and using the relations (22) and (23), we have the required relation (18). 
5. If v is taken large enough the transformations (14) will lead to the 

A(fe v„ 0** + m v ($ v , Vv , %r = ? l O* + <»i(QT*fi(v» 0, (25) 
PAiv, v» Q*v + Qv&, vv, 0p- = M£ + ^(m^{U 0, (26) 

vrj v 

<M&, v^ = *v(£ v , vv, 0^i (&, v^ = **(& vv, 0&(€v, vv, £)■ (27) 

We consider the effect of the transformations (14) on R in (18). Ex- 
press it in the form 

R(v, = n(v, On + (* 0n + i + 3 = ?S(v, 9, 


S(v, 0) * o. 

If (17, £)n contains no term in 77, the first transformation of (14) will al- 
low the factor £" to be taken out of S, leaving behind a constant term, 
and thus securing the form (25) at once with 


q x =p + n, r t = 0. 

Next, suppose (77, £)„ does contain terms in 77, but no term in 77", i. e. we 
can express it in the form 

where (77, £)„_,._, contains terms in both ^" _r_5 and £"- r -* and s > 0. 
Then if any transformation 

is applied, there can be divided out of (77, £) n the factor £" leaving behind 
as the term of highest degree one in rf*~*. This cannot be cancelled 
with any term from another part (77, £)„ +i , for any term from this would 
have as a factor tf after the £" has been divided out. As long, then, as 
the ?7 variable does not enter to the highest degree in the expression 
corresponding to (77, £)„ if n > 0, the degree of the S factor is decreased 
with each transformation, while the expouent of £ outside may be in- 
creased. Accordingly, by a finite number of transformations, we re- 
duce the S factor either to an E function or to an expression in which 
the 7; variable enters to the highest degree in the collection of terms 
of lowest order. In the former case we have the form required. In 
the latter case, suppose for convenience that this condition holds for the 
function £(77, £). By Weierstrass's Theorem we develop in the form 

S(?h = It + niOv"- 1 + + r n (0]£( v , 

= T( v ,0E( V) 0- . (28) 

Consider the n factors of T(rj, £), 

2 ? (^0 = n[, + fx(0]. (29) 


If the factors are not all equal, pair them off, so that in each pair there 
will be two different factors, leaving a number of equal factors : 

fr! + «ta(0] [*+**«)]} {Lv+st h (.Q]tv+su A (01}bi+s»(Qy- (so) 

Now, for each pair, 

^=[? + ^(0]D» + **(o:i, 

we have the relation 

N k +P k ( V ,i:) 9 ~ k = L k tt)$0, (31) 


since the two. factors are unequal. Then, by the same reasoning as used 


in 4, the succession of transformations (14) which leaves the degree of 
T unchanged will secure for equation (31) a form 

The left side of the equation is divisible by £ v , and so the right side 
must be, 

v = ^> 

and we have an upper limit for v, the number of transformations which 
leave the factor N k of the second degree, and as a result leave the func- 
tion T of the rath degree. So, unless the function T(rj, £) in (28) is 
composed of n equal factors of form 

bi + s (0?i ( 32 ) 

the transformation of (14) will finally reduce its degree. Then, by ap- 
plying the same reasoning to the resulting function, we see that finally 
the function corresponding to S(r], 'Q either becomes an E function or 
has besides the E factor a factor of form (32), thus securing the form 
(25) if we divide out the factor £<"»-i)»\ 

The condition (26) is secured by using on the second equation in 
(20) the same kind of reasoning as applied in 4 and 5. Then we take 
for v the larger of the two values required to secure conditions (25) 
and (26). 

C. — Further Transformations. 
6. A transformation 

& = £-<» 2 (0j (33) 

i) v — y] v — oj a (£) ) 
applied to the surface 

iu 5 will secure a form in which the singularity will be reduced by 

1) a further succession of transformations as in 3, 

2) the method of the Lemma, § 2. 

Let us consider here the case in which either r x or r 2 in (25) and (26) 
is zero. Then iu one of the equations a further succession of trans- 
formations of type (14) will not change the power of £ as a factor on 
the right ; and if there are /x such further transformations, the reasoning 


of 4 shows that the left side becomes divisible by £ (m-1) M. So we have 

(m—l)/x<q l or (m — 1)^ < y 2 

and thus an upper limit for /x, the number of transformations which 
leave the order of the singular point unchanged. 

Now, to consider the transformation (33), we see that it is a one- 
to-one transformation by which the surface remains analytic near the 
origin. (Dx (£) and w 2 (0 contain no constant term, for otherwise the 

rjv + wj (£) or £, + w 2 (£) 

could be combined with the E factor. Then the transformation (33) 
leaves the E factors still E factors, and the factors vanishing at the 
origin still vanishing there. Also, it is easily seen that this transfor- 
mation leaves the terms of type (£, rf) m still in the part (£„, tj v , £) m . 
Further, if the function «!>„(£„, -q v , £) goes over into X(£ v , rj v , £), we have 

9® v _9X _9X9l v _9X 
9 £ v 9i„ 9 £„ 9£ v 9 $ v 

and similar conditions hold for the partial derivative with reference to 
7/ v . Accordingly, if by the transformation (33) <&„(£„, Vv, £) goes over 
into £2(£„, rj v , £) we replace equations (25), (26), and (27) by 

1 v 
L v (i V} £, t)X(l, Vv , + M v Q vi y v , 0— - = frvSiEfa 0, (34) 

9t v 

P v (l, vv> QBQ„ £,, £) + &<&, Vv, 0-J?= ^~^E($ V , 0, (35) 

9rj v 
Q(|*» Vv> = XQv* Vi"> CAlC?** V"> — &(€vj t]v, O-^aClfj Vv, 0- ( 36 ) 

Now, in a further succession of transformations of type (14) on the 
surface f2 (£„, Vi>> £) — 0, if there enters either a y or a 8 not 0, then on 
the right side of equation (34) or (35) the only factor remaining outside 
of the E factor is a power of £, and we must finally have a reduction as 
shown above. So it is only in the case in which all the y'a and S's of 
the later transformations are that we are not already sure of reducing 
the singularity. Now if in £2 (f„, r),,, £) there is any term of degree less 
than m in £„ and -q v combined, such a succession of transformations must 
reduce this term to a degree less than m and thus reduce the singularity. 


For suppose such a term to be aljrjjt, h , where /+ g < m. Then, by 
a succession of p transformations such as defined, we have 

L = £, p $ v+ p, V" = £ p yv+pj 

(derived from form of (19) when all y's and S's are 0). Substituting 
this in the expression above we get 

a? v+P V,,+p£ 
But we must divide out of this £ mp , so that we have left the term 

n t } J yh+piZ-hg-m) 

This term could not combine with any other derived in a similar way, 
for if we had another term b$* rj g £\ we should get 

7 >/ 9 yk+p{f+g—m) 

o? v+p v v+P £ 

and this would not combine with the other unless k = h. Now, if the 
degree of the singular point is not reduced, we must have for the sum 
of the exponents 

f+g + h + p(f+g — nij^rn 

or (p + 1) (m — /— g) ^ h, 
and as m > f + g 

+ 1^ 

»» — /— g 

thus securing an upper limit for p, the number of transformations which 
leave the term and the singular point of the mth order. 

So it is only in the case in which all terms of Q (£„, r/ v , Q are °f 
degree not less than m in £" and rj v together that we do not have a re- 
duction of singularity by the succession of transformations of type (14). 
But, in this exceptional case, we have the conditions of the Lemma of 
§ 2, where in equation (0) we take 

lv = a? a , Vv = z-i, t = y-i, 
the singular line being 

^ = 0, |„ = 0. 

There is in D, (£„, rj v , £) a term in £ v m , and so the expression q (y 2 ) 
does not vanish when y 2 = 0. Accordingly, within a neighborhood 
about this point, we can break up the singularity by the methods of 


§ 2. Further, since the expression (f„, rj v ), n is not composed of m equal 
factors, the part 

q (0)x a m i + q x {0)x^- l z + + ?«h(0)si"i 

from (6) which corresponds to (£„, n v ) is not composed of m equal factors, 
and the resulting curve in (k) 

*3 CTl + niy^x^- 1 + + r mi (j/ 2 ) = 

has not m equal roots when y 2 = 0. So a single transformation of the 
kind in § 2, 3, reduces the singularity in the neighborhood considered 

7. The neighborhood of the original singular point is mapped upon 
a finite number of neighborhoods of simpler points. 

At every stage the function (£ M , rj^, *£),„ contains the terms of the 
type (£, rj) n found iu the original equation (13). So there is but one 
singular point of the m-th order in the finite region of the 77^-plane. 
Further, the equation (^, 1, Q m = for the value £ = cannot have 
m equal roots since (£, v) m is not a perfect m-th. power of a linear factor. 
Accordingly, the transformation corresponding to (8) in § 1, 4, cannot 
produce a singular point of the m-th order. So, at each step, the 
neighborhood of the singular point is represented by a number of regions 
as in § 2, C, in which but one of the points of class 1) is of the mth order. 
Further, the extra transformations (33) carry the neighborhood of the 
singular point over into that of the new point. So, by combining all 
the representations, as the singularity is finally reduced, we have the 
original neighborhood mapped upon a finite number of regions as in 
§ 2, C, in which all points of class 1) are of order lower than m. 

§ 4. 

A. — The Singular Points of Special Type (continued). 

1. Case B. — The m linear factors of (f, rj, £) m are all equal. 
The surface can be expressed in the form 

*(& v, = [F + Pn(a, Of- 2 + + Pm (r,, 0] #(6 v, 

= X(£, v ,0£&vU) = 0, (37) 

where, in X, $'" is the only term of degree m. 
If it were iu the form 

f(u, v, w) = (ail + (3v + yw) m + (it, v, w) m+1 + = 0, 

as one of the three numbers, a, (3, y, is not zero, suppose a = 0. 


Then by a linear homogeneous transformation 

u = au + (3v + yW 
v = v 

w = w 

we secure the form 

f(u, v, w) =f(u, v, w) 

— u m + («, v, w) m+l + 

By Weierstrass's Theorem we can express this in the form 

f{u, v, w) = \u m + p, (v, w) u" 1 - 1 + + p m (v. w)-] E{u, v, w). (38) 

Now, in the exjjression 

p K (v, w), A = 1, 2, m 

there is no term of degree less than A + 1, for otherwise on account of 
the constant term in the i£ factor, there would have to be present in^a 
term of degree < m containing v or w. 
Make in (38) the transformation 

u + r* Pi ( v w ) 


As pi (v, w) contains no term of degree less than 2, by the considera- 
tion above, f goes over into form (37). 

B. The Quadratic Transformation. 
2. The transformation 

£ = i£> v — v& 

applied to <E> (£, 77, £) secures the form 

*(*, v, = *"•*(£ v, = £*[?" + £*(!, v, 01 (39) 

Here the curve <f> Q, ij) = becomes | m = 0, and so, applying the 
Lemma of § 2 to a circle in the y^-plane however large, we have within 
it but a finite number of singular points to treat further. But one such 
circle is needed, for by taking it large enough we can deal with all of 
the ^-plane outside of that circle by the transformation 

So we need to consider for further treatment only a finite number of 
points along the line $ = 0, and the point at infinity. 


3. The quadratic transformations to be used are of two types 

1) £p =s &+1&4 Vn = Ofo+1 + VrO &u ( 40 ) 

2) in — in+iVnt Cm = (&+1 + e f.+i)Vn' ( 41 ) 

In a succession of transformations of type (14) we see that yx = 0, 
since the first set of points is taken on the line |" = 0. Further, sup- 
pose after the substitution q — 8 X = ^ in <I> of (39) the expression 

(!, 171 Qm 

contains terms besides the £ m ; then it cannot be composed of m equal 
linear factors, for that would require a term containing f m_1 ; but no 
such term can arise from the factor X of (37), and, on the other hand, 
it could not be the product of a term from X by a non-constant term of 
the E factor, for then, on account of the constant term of the E factor, 
there would have to be present in <f> a term of degree lower than m. So 
as soon as the function corresponding to <f> of 4> contains more than the 
mih power of the £ variable, the function corresponding to (£, 77, £)„, iS 
no longer the product of m equal linear factors, and we have one of the 
cases treated earlier. 

The same considerations apply to the transformations corresponding to 
type 2), since, when the transformation which deals with the infinite 
region is introduced, the first one of that order is of form 

Accordingly, the most general succession of transformations here is 
one in which groups of types 1) and 2) alternate. We shall call them 
the £ and q types respectively, and when a change is made from one type 
to the other, we shall speak of it as a reversal of type. 

We shall treat the subject in two cases, first supposing that there is 
no reversal of type in the succession of transformations used, and later 
supposing that reversals of type occur. 

C. — Succession op Quadratic Transformations in avhich 


4. After a sufficient number of quadratic transformations the surface 
can be reduced to the form 

-, v + • • • + v v 


[(C + ~< 2 & E (n»> C" 2 +■■•■• + % ? v E(ji*, i)] m» i, 0> (42) 


while all later transformations can be taken of the type 

£ M = £y+lL rjy. = Vn+iC (43) 

After v transformations of type (40), since there can be no interchange 
of terms among the coefficients of the different powers of the £ variables 
in the X factor of (37), the surface will take the form 

[C + v» (v* C 2 + + P™ (Vv, 0] * (&, to = 0. (44) 

Now by the same reasoning as used for the function R in § 3, 5, if v is 
taken large enough, the coefficients of the powers of £„ in X v will all be 
of the type 

s = 2, 3, m. 

For any one of the functions 

there is a determinate succession of transformations of type 

Vy = £(Vn+l + <V+i) 

which will leave it of the same degree after the £ is divided out, all 
others reducing the degree at once , i. e., if 

Vy + v (£) = Vy + <*i £ + tt 2 £ 2 + , 

we must take 

Vy = UVy+1 — "i)» 
rjy+1 = £(Vy+2 — a 2 ), 

So, unless the factors 

V" + v, (Oj s = 2, 3, m 

are all equal, we must have finally some coefficient of a power of £„ with 
the rj v present only in the E factor, and by taking y large enough we 
come to a point where all the factors 

V' + v *(0> S = 2, 3, m, 

are equal, some of them possibly having zero exponents. 
Then we use the transformation 

np + v.OO^n, (45) 


and arrive at the form (42) required. Now any further transformation 
of type (40) in which the 8 is not zero will leave the -q variable present 
only in the E factors, so that the general term (after the first) of the 
function X v is of type 

pUfayQC-, s = 2,3, m. 

Suppose, after this, there are p transformations of type (40). Then the 
corresponding term after the factor £ mp has been divided out is 

9%+{ m—s)p—mp jg, on. gm— s 

and if this is of degree not less than m, as it must be if we are not to 
secure reduction, we have 

m — s -f <7s — P s = m 

or p < — » 

~ s 

thus securing an upper limit for the number of transformations of type 
(40) which do not give reduction of singularity. Accordingly, after the 
form (42) is reached, it is only when all later S's are zero that we are 
not sure of reduction.* 

5. A sufficient number of transformations of type (43) applied to (42) 
secures either 

1) reduction of singularity, or 

2) the condition that for some term (the rth) of the X factor 

> s = 2, 3, m. 

r ~~~ s ) 
If, for any term 

a transformation of type (43), after the factor £'" has been divided out, 

„Pr yQr+Pr—r jfi / y\ j.m-r 

decreasing the exponent of I by r — p r . This decrease takes place at 
every such transformation, and thus the exponent of £ must finally be 

* We do not need to consider the possibility of having all the coefficients of the 
powers of £„ lower than the m-th vanish, for then the function X v would have 
m equal factors £„ and this case has been excluded. 


reduced to a value q' r less than r — p r , in which case the sum of the 
exponents of the three variables, 

p r + q' r + m — r, 

is less than m and reduction ensues. So it is only in the case in which 
for every term 

p s > s, s = 2, 3, m, 

that we are not sure of reduction. Suppose the number of transforma- 
tions after this point to be n. Then we get for the new exponent of £ 

9s + n (Ps~ *)• 
Now by taking n large enough we can make the quotient 

n (P* - *) + 9s 

7) ™— S 

have the lowest value for the term in which — is lowest, while if 


this is the same for two or more terms, we can make the fraction above 
lowest for the one in which — is lowest. Accordingly, by a finite 
number of transformations of type (43) we secure the condition that 

V — T V . Q 

— and so — is lowest in the same term in which — is lowest. 

r r 

6. A succession of transformations of type 

& = | M+ i£, (46) 

followed by a succession of type 

£1 = ^+117, (47) 

secures the surface with condition 5, 2) in the form 

J. (48) 

where for some particular term in X p , the rth, 

Pr <r, q r <r. j 

Consider the surface (42) with the condition 5, 2), the sth term being 

and suppose we apply to the surface n transformations of type (46), 
dividing out each time the factor £"'. The resulting term is 

If n is taken large enough, the exponent 

is made less than s, so that we have 

s > q s — ns > 0, 

or Si— I <n<Sl. 

s s 

So the term for which — is least is among those first reached in which 

s ° 

the new exponent of £ is lower than s. 

In the same way we show that, by applying a succession of transfor- 

mations of type (47), the term for which — is least is among the first 


lot reached for which the new exponent of -q is less than s. But, by 

condition 2) in 5, — and — were least in the same term. So we secure 

' s s 

the surface in form (48). 

7. A further succession of quadratic transformations of type (43) as 
applied to the surface in form (48) will reduce the singularity. This 
follows at once by the reasoning in the first part of 5. 

D. — Succession of Quadratic Transformations in which 


8. A succession of transformations in which there is a sufficient num- 
ber of reversals of type will secure a surface of type (42). 

If there is but a finite number of reversals, after the last one we are in 
the same positiou as at the start in 4, and the succession of trans- 
formations which follows, not having any reversal of type, will enable us 
to secure the condition derived by the method of 4. So we need here to 
consider only the possibility of an indefinitely large number of reversals 
of type. 

In equation (37) consider any one of the coefficients 

p r ( V ,0 = ?Pr(v,Q = tl(v,0n r + (v,On r+ l + ] 

where p r (v-> °) ^ °- 

A transformation of type (40) will give for p r a function from which we 


take out the factor C, the other factor being of degree less than n r unless 
the part (7/, £) nr has n r equal linear factors. For, if 


(V> t)n r — n (a p rj — jB pt) 

and not all the linear factors are equal (or linearly dependent), then the 

V = C(vi + Si) 

C II (a p r/ x + dp^ — /3 p ) 
P = l 

and leaves an absolute term in any factor for which 

a p Sj 4= /3 P , 

thus securing in the product of the factors terms of degree less than n r . 
Also the degree might be lowered on account of terms in some later part 
as (77, £,)n r +k- But, if all the factors of (7/, £)«,. are equal (or linearly 
dependent) and 8j is taken so as to satisfy the condition 

a P^i = fip, p = 1» 2, « r , 

then after the factor C is divided out, we have left but one term in rj 1 nr , 
which cannot cancel with any term from another part of the function, as 
all later terms have as a factor some power of £. Accordingly a suc- 
cession of transformations of type (40), if it does not reduce the degree of 
the part not divisible by £, must leave a term in rj Br , Now when the 
reversal of type is first made, the e of (41) is zero, as is seen by con- 
sidering the use of transformation (8) § 1, 5. Then we take out a 
factor 7/ "'' and leave a constant term. So a succession of transformations 
which contains reversals of type must reduce the degree of the function 
p r (possibly to zero), except for factors taken out which are powers of 
the r/ and £ variables. Accordingly, by a succession of transformations 
containing a sufficiently large number of reversals of type, the coefficient 
p r must be reduced to the type 

9. All further transformations to be considered may be taken of the 

in = t».+\yi, £m = C+1^7- ( 50 ) 


For if a transformation of type (40) or (41) in which the 8 or c is not 
zero were used, we should have in all the coefficients of X v in (42), out- 
side of the E factor, only powers of one variable. Suppose it to be £ ; 
then, by means of a succession of transformations of type (46), we can 
reduce some term to a form in which the exponent of £ is less than r, 
and thus secure a reduction of singularity. 

10. A sufficiently long succession of transformations of types (49) and 
(50), applied to surface of type (42), unless it first secures reduction 
of singularity, will secure the condition that, for some term (the rth), 

s = 2, 3, m. 


r s J 

Consider the two terms 

f&sh o r~ s , v pt t qt E{-n, o r~* 

Any transformation of type (49) leaves the p a and p t unchanged, and 
increases the 

q s by p s — s, 

9t " Pt — t. 

Any transformation of type (50) leaves the q„ and q t unchanged, but 
increases the 

p, by q s ~ s, 

Pt " q t - 1. 


q,. — r 

r = 2, 3, m, (51) 

So, for each transformation of type (49) the K r is increased by the Il r , 
and for each transformation of type (50) the II r is increased by the K,.. 
We shall show that finally we must have one of two conditions 

«) n s > 17„ K, > K t , 

b) U s <U t , K s < K t . 

Suppose, at any stage, neither of these conditions holds, and we have, 
for example, 

n s > n„ K, < K t . (52) 


Then, for a transformation of type (49), supposing the new K's to be 
K,', K/, we have 

K,' = K, + IT S , 

K/ = K, + IT,, 
and so 

K/ — K/ = K, — K s - (n, — n f ) < K ( - K s . 

Also, for a transformation of type (50), if the new El's are Uj IT/, we 

UJ = n. + K„ 

uj = U t + K„ 


IV - uj = u s -u t - (k, - k.) < n 3 - n,. 

So when a condition of type (52) holds, any transformation applied will 
reduce the difference of either the ITs or K's, if in fact it does not 
change the sign of the difference. Further, the reduction is each time 
by a value not infinitesimal, for it is at least 1 j st, as is seen by con- 
sidering the values of K r and IT,, in (51). So the succession of trans- 
formations of whatever kind must finally reduce the difference of either 
the II's or the K's to zero, or change its sign, and then we secure either 
condition a) or b). 

When one of these conditions has once been secured, any further 
transformation will not change it; for, in condition a), a transformation 
of type (49) will add at least as much to the K s as to the K„ and so 
retain the inequality of the same order, and similar conditions are seen 
to hold in the other cases. Also, as one of the conditions «) or b) must 
hold finally, whatever the pair of values s and t, we shall have some 
value as r such that 

n,. < IT S , K, < K„ s = 2, 3, m. 

from which follows the required condition 

Pr K Ps 

r ~~ z s 

9r < 9 1 

2, 3 m. 

11. The method of 6, applied to the surface resulting from the treat- 
ment of 10, will secure the result of 6. It may be that already either 
p r < r or q T < r, but in such a case the number of transformations of 


type (46) or (47) can be considered zero, while in the other case we 
have exactly the initial conditions of 6, the result of which then can be 
secured in any case whatever. 

12. In tlie case of surface (48) any succession of transformations of 
types (40) and (50) will finally reduce the degree of the singular point. 

Consider the term 

Any transformation of type (40) adds to the exponent of £, p r — r, and 
as p r < r, the exponent of £ is reduced. In the same way we see that 
any transformation of type (50) reduces the exponent of the 77 variable. 
So in any case, by virtue of the reduction of degree, we must have finally 

Pr <r — q r or q r < r — p r , 

in either of which cases the sum of the exponents of the three variables 

(m — r) + p r + q r 

is less than m, and we have reduction of the singularity. 

§ 5. 

Parametric Representation of the Neighborhood of the 
Original Singular Point. 

We have shown that in all cases T, the neighborhood of a singular 

point, can be mapped upon a fiuite number of regions t u t. 2 , t v as 

defined in § 2, C. Apply a properly chosen transformation to each point 
of class 1) and repeat the operation on each set of resulting points of the 
same class as they are formed. We have proved also that after a finite 
number of operations all the resulting points of class 1) are of order 
lower than m. Then, by continuing the process, it follows that, after a 
finite number of transformations, all points of class 1) must disappear, 
and so we shall have left only regions of class 2). Each of these regions 
admits of representation by means of a finite number of sets of para- 
metric formulae of tj'pe (A). 

Classify all the singular points which present themselves in groups as 
follows : — 

In the first group, place the original point; in the second, all singular 
points derived from it by the first quadratic transformation, together witli 
whatever auxiliary transformations accompany it ; these points corre- 
spond to the singular points of the curves that represent the irreducible 


factors of <j> (£, rj), to the points of intersection of two such curves, and 
to the points of class 1) in § 2, 1. In the third group place all singular 
points derived in a similar way from those of the second group, etc. 

Suppose n to be the number of the last group in which there are 
singular points. From what we have proved, n must be finite. 

The neighborhood of a point in the wth group is represented by the 
neighborhoods of a finite number of regular points, together with a finite 
number of regular regions, and so by a finite number of parametric 
formulae of type (.4). The neighborhood of a point in the (ra — l)st 
group is represented by the neighborhoods of a finite number of points of 
the ?ith group, together with a finite number of regular regions, however 
small the neighborhoods of the singular points are taken ; but as the 
neighborhood of any point in the wth group is represented by a finite 
number of parametric formulae of type (A), the same follows for any 
point of the (n — l)st group, using the intermediate transformation to 
get the parametric formulae. 

This reasoning can be carried on until the original singular point is 
reached, since the mapping of the neighborhood of the original point 
upon a finite number of regions of classes 1) and 2) applies to each of the 
later singular points also, and then furnishes the step by which we know 
that we can always pass from the (y + l)st to the vth group. 

Thus we have the coordinates £, rj, £ of the surface 

expressed in parametric formulae of the desired type, the parameters 
being in general coordinates of points of some simple surface. Then by 
using the intermediate transformations connecting x, y, z with $, rj, £, we 
represent the first set of coordinates in the desired form. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 12. — December, 1901. 



By Edgar W. Olive. 



By Edgar W. Olive. 

Presented by Roland Thaxter. Received November 9, 1901. 

Owing to unavoidable delay iu the publication of a monograph of the 
Acrasieae and their allies which the writer has in preparation and for 
which figures have already been drawn, the following preliminary 
synopsis, which includes all the known forms and which will be sup- 
plemented as soon as possible by the more extended paper, has seemed 
advisable. This investigation was undertaken some years since at the 
suggestion of Professor Thaxter, and a majority of those species that I 
have myself studied have been kept under observation in pure cultures 
for a long period, so that the constancy of the characters distinguishing 
them has been definitely determined. As far as I am aware only one 
member of the group has been heretofore reported from America, 
although certain of them are very abundant in laboratory cultures. Of 
the European representatives several remain unknown except through 
the original diagnoses, which are unfortunately, in a majority of cases, 
meagre and unaccompanied by figures. 

A comparison of the conditions presented by the individuals which 
constitute the so-called fructifications of these organisms indicates that 
the term spore cannot be properly applied to them in all cases. In the 
genera Sappinia and Guttulinopsis the individuals, even in mature 
fructifications, are merely slightly contracted and hardened, secreting no 
definite wall. At germination such resting individuals, therefore, gradu- 
ally assume the form of a vegetative amoeba without casting off a spore 
wall of any kind. In order to distinguish these bodies from true spores, 
such as occur in a majority of the genera, as well as from the transi- 
tory resting conditions of isolated vegetating amoeba? which were first 
characterized as " microcysts " by Cienkowsky, the term pseudospore is 


here employed, since it expresses with sufficient exactness the actual 

It will be noted further that in characterizing the Acrasieae as a 
whole, emphasis has been laid on the fact, usually overlooked in accounts 
of these organisms, that the vegetative stage ends before the pseudo- 
plasmodium condition begins. The latter, therefore, is a phenomenon con- 
nected not with vegetation but with fructification, and is by no means 
homologous with the plasmodium of true Myxomycetes; nor is it com- 
parable to the vegetative net-plasmodium of the Labyrinthuleae. 

I have followed Zopf, moreover, in characterizing as a " net-plasmo- 
dium " the peculiar form of association occurring in the Labyrinthuleoe, 
although it appears to be doubtful whether, in all cases at least, the con- 
dition thus distinguished represents a true fusion, or whether the relation 
is merely one of contact. 


Amcebas of the usual irregular myxamceba form or more or less reg- 
ular and spindle-shaped, never possessing a swarm spore stage, forming 
either a pseudoplasmodium or a net-plasmodium ; resting bodies borne 
in sessile or stalked sori, which are either naked or imbedded in a 
gelatinous matrix. 

ACRASIEiE Van Tieghem. 

Saprophytic, usually coprophilous, organisms, having two definitely 
recurring stages, — a vegetative period, in which independent myxamoebaa 
crawl about by means of amoeboid movements and undergo multiplication 
by division ; and a fructifying period, in which the myxainccbse typically 
aggregate into colonies called pseudoplasmodia and form either spores 
or pseudospores, held together by a mucus substance, and borne in 
stalked or sessile naked masses, or sori. 


Myxamcebas comparatively large, with lobose pseudopodia. The 
resting sta^e consisting either of a single encysted individual or of 
many individuals encysted in masses at the ends of projections of the 

This group is included here only provisionally, since the amoeba? 
normally become encysted singly, thus forming microcysts, and do not 
show the characteristic phenomenon of aggregation, or colony formation. 
The aggregations which, it is true, often occur at the distal ends of 


small projections above the surface of the substratum, are not due to 
any chemotactic stimulus such as must be assumed to cause the formation 
of true pseudoplasmodia, but, although they may perhaps suggest the 
possible beginnings of such conditions, are probably accidental, resulting 
rather from a tendency of the arnoebaj to seek drier situations at the 
period of fructification. 

SAPPINIA Dangeard (1896). 
Characters of the order. 

Sappinia pedata Dangeard. 
Le Botaniste, 5 Ser. p. 1-20. 5 Figs in text. 1896. 

Amoeba? forming resting conditions of three kinds : " amibes pedicel- 
Ices," in which they are transformed into a pear-shaped body without 
definite wall raised above the substratum by a stalk of about equal 
length ; " hjstes pedicelles" in which they are similarly modified but 
which form a definite wall about the oval body; and '' spores," in which 
groups of individuals become encysted at the ends of projections from 
the substratum. 

On dung of horse, cow, dog. France ; Russia; Massachusetts ; Indiana. 

At least two species of this genus appear to be common on various 
kinds of dung in this country, but owing to the fact that Dangeard gives 
no measurements I have been uncertain which of them should be referred 
to S. pedata. In both forms resting bodies comparable to the aggregated 
"spores" occur, as well as u amibes pedicellees" although I have not as 
yet observed the definitely walled "kystes" which Dangeard appears to 
distinguish from them. 

The larger and more frequent of the American species, which I have 
assumed to beloDg to S. pedata, has the following measurements : stalk 
of the "amibes pedicellces" 30^-125^, head 30^-60^ long; rounded 
individuals (" spores ") of the aggregations 20^-50^ in diameter. 


Myxamoebse either limax-shaped, without pseudopodia, or of the 
ordinary form with rounded or lobose short pseudopodia. The sori, 
irregular in shape or spherical, sessile or stalked, consisting of either 
spores or pseudospores. 


Myxamceba3 having lobose pseudopodia. Sori sessile or stalked, com- 
posed of pseudospores, those of the stalk usually slightly elongated. 


Guttulinopsis vulgaris nov. sp. 

Sori usually stalked, sometimes sessile, about 150^-500/* in height 
X 150//.-4.CKV broad. Fructifications varying in color from whitish to 
dirty yellowish according to the character of the substratum and the dry- 
ness of the sorus. Pseudospores usually irregularly spherical, about 4/z- 
8p in diameter. 

On dung of horse, cow, pig, mouse, etc. Cambridge, Mass ; Alabama j 
Indiana ; Maine ; Porto Rico. 

This form, which has conspicuous fructifications so large that they 
may be readily seen with the naked eye, lias been met with very fre- 
quently on fresh cultures of various kinds of dung. Although Guttulina 
aurea Van Tieghem may prove to be identical with the ahove species, 
the fact that, according to the original description, it possesses resting 
bodies which are characterized as " spores," having a golden yellow color, 
renders it improbable that the two forms are the same. 

Guttulinopsis stipitata nov. sp. 

Sori yellowish white, long stalked, the stalk composed of individuals 
similar to those of the head. Sorus about 1 mm. -1.2 mm. high; the 
stalk about 800/a long, the head 250/* in diameter. Pseudospores spher- 
ical, 3^-5^ in diameter. 

On dung of dog. New Haven, Conn. 

This species, the largest representative of the genus, has been met 
with but once, and is founded on a mounted specimen and dried material 
collected at New Haven some years ago by Dr. Thaxter. 

Guttulinopsis clavata nov. sp. 

Sori yellowish white when young, comparatively long-stalked, the stalk 
composed of a column of slightly elongated individuals surrounded by 
mucus. The stalk-cells held within the peripheral mucus adhere together 
after the deliquescence of the pseudospores of the head, forming at the 
apex a rounded or conical columella of elongated adherent cells. Sorus 
about 400 i u-800 i u in height, the stalk about 170^-250//. long, the head 
I00 ( u-400 i u in diameter. Pseudospores of the head somewhat broadly 
oval, 3//.-4/A X 6// - 7/a, or spherical, then 4^-5//. in diameter ; those of 
the stalk about 3fi-Ofi X 7/j-10ix. 

On dung of dog. Cambridge, Mass. ; Indiana. 

This distinct species is frequently met with in fresh cultures of the 
dung on which it has its habitat. The base of the stalk is often imbedded 


in an abundant mucus, which is especially noticeable when it swells after 
being placed in water. 

GUTTULINA Cienkowsky (1873). 

Myxamcebre limax-shaped, without pseudopodia. Sori irregular in 
shape or spherical, sessile or stalked, composed of spores which have a 
definite protective cell-wall. The cells of the stalked forms somewhat 
differentiated in shape. 

Guttulina rosea Cienkowsky. 
Trans. 4th Session of Russ. Nat. at Kazan, 1873. 

' ' Sori short-stalked and rose-colored ; head IQQfx long, supported upon 
a stalk of about equal length. Spores of the head spherical ; those of 
the stalk closely laid and wedge-shaped." 

On dead wood. Russia. 

Known only from the original description above quoted. 

Guttulina protea Fayod. 

(Copromyxa protea Zopf.) 
Bot. Zeit., 11, p. 167-177. 1 Plate. 1883. 

Sori l-3mm. high, sessile or short-stalked, of somewhat irregular form, 
yellowish white, with crystalline lustre. Spores 9/aX14u; hyaline, 
colorless or slightly yellowish, more or less oblong or oval, bean-shaped, 
or almost triangular in outline. 

On dung of horse and cow. Germany. 

This form, which is known only from Fayod's original description, is 
retained under its original name, notwithstanding the fact that it has 
been separated by Zopf under the name Copromyxa on the ground that 
the " myxamcebae undergo no differentiation into stalk and head cells, 
whereas in Cienkowsky's form, there is a slight differentiation." The 
fact that certain species of Guttulinopsis show both stalked and sessile 
forms in the same culture diminishes the importance of the stalk as a 
character of generic value and justifies the resumption of the original 
name given by Fayod. 

Guttulina aurea Van Tieghem. 
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. 

" Guttulina aurea has its fruit pedicelled and resembles closely G. 
rosea, but differs in color. The spores spherical, Ap.-6fA, golden-yellow. 
Upon dung of horse." France. 


Guttulina sessilis Van Tieghem. 
Bull, de la Soc. Bat. de France, XXVII. p. 317. 1880. 

" Fruit sessile ; a simple droplet of pure white, resting directly on the 
substratum. Spores oval, colorless, aggregated in a sphere and cemented, 
as in the preceding species, by a gelatinous substance ; 4/a X 8/t. On the 
integument of beans in a state of decay." France. 

Guttulina aurea and G. sessilis are known only from the original 
descriptions above quoted. 


Myxamcebce possessing slender elongated pseudopodia. Sori consist- 
ing of spherical masses of spores or of a chain of spores ; stalked, the 
stulks composed of distinct parenchyma-like cells with cellulose walls. 

ACRASIS Van Tieghem (1880). 

Spores concatenate, terminating an erect simple filament, consisting of 
a single row of superposed cells. 

Acrasis granulata Van Tieghem. 
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. 

Spores spherical, with a slightly roughened or granular wall, having 
acuticularized external portion of deep violet color ; 10^-15^ in diam- 
eter, often unequal in the same chain, the chain varying much in the 
number of component spores and cells. 

On a culture of beer yeast. France. 

Known only from the original description. 

DICTYOSTBLIUM Brefeld (1869). 
Sori stalked ; the stalk simple or only occasionally bearing irregularly 
disposed branches ; luxuriant fructifications frequently gregarious. Sori 
spherical, or subglobose. 

Dictyostelium mucoroides Brefeld. 

(Ceratopodium elegans Sorokin.) 

Abh. d. Senck. Nat. Ges., VII. p. 85-108. PI. I-III. 1869. 

Sorus and stalk white, or when old, yellowish ; the fructifications 
varying in height from 2-3 mm. to 1 cm. or more. Spores oval or 
elongated ellipsoid, 2A/x-S^ X 4/x-6/x. 


On the dung of various animals, such as horse, rabbit, clog, guinea pig, 
grouse, etc. Also found on cultures of yeast, paper, fleshy fungi, etc., in 
a state of decomposition. Germany, Russia, common in America. 

This very common species is extremely variable in the size of its spores 
and fructifications. The limits of the spore measurements as given by 
Brefeld in his original description have been therefore somewhat 

Dictyostelium sphserocephalum (Oud.) Sacc. and March. 
{Hyalostilbum sphcerocephalum Oudemans.) 

Aanw. Myc. Nederl., IX.-X. p. 30. PL IV. 1885. 

Sorus white; when old, yellowish or greenish-white. Stalk frequently 
very long and luxuriant, varying from 2 mm. to 1.5 cm. Spores oval, 
rarely spherical, or sub-inequilateral, 3^-5/x X 5/a-IO/a. 

Dung of mouse, (common), rat, bird, toad, deer, turtle, muskrat, etc. 
Belgium ; Cambridge and Boston, Mass. ; New Hampshire ; Florida ; 
Pennsylvania ; Liberia. 

In the above description the limits of the measurements of spores and 
of the length of stalks are greater than those given by Marchal, by 
whom the maximum length of the spore is stated as 8^ and that of the 
stalk as 5mm. The measurements of the fructifications are certainly 
more variable than indicated by Oudemans. This species was founded 
by Marchal from the fact that the spores differed in size from those of 
Dictyostelium mucoroides, which he states to be only about one-half as 
large. As will be seen by the measurements given above, this difference 
is by no means as great as indicated ; and, although the present arrange- 
ment is retained for the present, it may prove desirable to unite these 
two variable species. 

Dictyostelium roseum Van Tieghem. 
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. 

" Spore mass spherical, of a bright rose color. Spores elongated oval, 
4/x X Sp.. On the dung of various animals ; especially on rabbit dung, 
in company with Pllobolus micros'porus.' n France. 

Dictyostelium lacteum Van Tieghem. 
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880. 

"The mass of spores forms a milk-white drop at the summit of a stalk 
which I have always seen composed of a single row of cells. Spores 


colorless, spherical, very small, 2[x-3fi in diameter. This form has 
been met with several times on decaying agarics." France. 

Neither of the two ]5receding forms have been found in American 
cultures, hence the writer can add nothing to our knowledge concerning 

Dictyostelium brevicaule now sp. 

Sorus white ; stalks 1-3 mm. high. Spores oval, 3/^-4/j. X 4//-7/Z 
or rarely spherical and 3^-4//. in diameter. 

Dung of sheep and goat. Cambridge, Mass. 

A small, erect fructification, quite constant in the possession of a short 
rather rigid stalk bearing a sorus of comparatively large size and very 
different in aspect from the long, luxuriant, frequently flexuous, fructifi- 
cations of D. mucoroides and D. sphcerocephahcm. Throughout the four 
years that this species has been kept growing in laboratory cultures, it 
has retained its original distinct characters. 

Dictyostelium purpureum nov. sp. 

Sorus and stalk purplish or violet ; when mature, almost black. Spores 
oval, rarely somewhat inequilateral, 3/*.-5/x X 5/x-Sfx. 

Dung of mouse, toad, cow, horse, sheep, muskrat. Cambridge, Mass.; 
Indiana ; Florida. 

This distinct species, well-marked by its color, was collected in Aug- 
ust, 1897, in Crawfordsville, Indiana, on mouse dung cultures, and in 
October of the same year by Dr. Thaxter in Eustis, Florida, on toad 
dung. Both forms have been cultivated ever since in the laboratory, 
with no particular precautions as to the dissemination of the spores, and 
it is not impossible that the fructifications which appeared at Cambridge 
on sub-strata other than the two just mentioned represent laboratory 

Dictyostelium aureum nov. sp. 

Mature sori light to golden yellow, 1.5mm. -4mm. high. Spores oval, 
or frequently inequilateral, 2.5^-3^ X Ofi—Sfi. 

Mouse dung from Porto Rico. 

This species, communicated by Dr. Thaxter, is quite well defined 
through the color of its fructifications, but especially so by its myxamcebse 
and its manner of growth. It matures very slowly on a horse dung de- 
coction or on other media especially favorable for the rapid development 
of the common species ; while the myxamoeboe, instead of possessing the 


usual form with elongated, sharp pseudopodia, are in general irregularly 
lobed and nodulated, even when growing under normal conditions. Such 
irregular shapes are similar to those assumed by the rnyxamcebre of other 
species when they are growing under such abnormal conditions as are 
furnished by an insufficient water supply. 

POLYSPHONDYLIUM Brefeld (1884). 

Sori spherical, borne terminally on primary and secondary stalks, the 
latter branching in whorls from the main axis ; the fructification occa- 
sionally simple as in Dictyostelium. Whorls varying in number from 
1-10, and the number of branches in each whorl from 1-6. 

Polysphondylium violaceum Brefeld. 
Schimmelpilze, VI. p. 1-34. PI. I, II. 1884. 

Sori and stalks purplish or dark violet, varying in height from about 
^cm.-2cm. ; sori about 50/x.-300^u in diameter. Spores elongated oval, 
2.0/i.-5/x X 6ix-8fx. 

On dung of horse, bird, sheep, toad, muskrat. Italy, Maine, New 
Hampshire, Massachusetts, Florida. 

The limits of spore measurements as given by Brefeld have been in- 
creased here as in other instances. The form growing on bird dung, 
brought by Prof. F. O. Grover from Center Ossipee, N. EL, and the 
Massachusetts form on the dung of muskrat, seem to correspond very 
closely to the type description. The spores of the Maine and Florida 
forms are somewhat smaller, while the general aspect of the fructifica- 
tions is different in that they are more delicate and less luxuriant and 
the sori have a less diameter than those of the type. These differences, 
however, seem hardly more than varietal. 

Polysphondylium pallidum nov. sp. 

Sori and stalks white, the sori about 50/^-80/x in diameter. Spores 
oval, 2.5/x-3/x X 5^-6.5/^, or occasionally spherical, about 7fx-8fi in 

On duug of ass, rabbit, muskrat. Liberia, Africa ; Arlington and 
Stony Brook, Mass. 

This delicate species is well characterized by the small size of its sori. 
In an interesting specimen, found by Mr. A. F. Blakeslee on muskrat 
dung, luxuriant fructifications showed that some of the branches them- 
selves bore several whorls of branchlets. That this doubly verticillate 


character was not constant, however, was proved by growing the form 
on a sterilized nutrient medium, on which the fructifications showed 
simply the normal method of branching. 

Polysphondyliura album nov. sp. 

Sori and stalks white, the sori 100^. to 200^ in diameter. Spores oval, 
2.5^-3/x X 4^-5.6^. 

On dung of toad from Eustis, Florida. 

Although the two forms above described have some features in com- 
mon, their gross characters are such as to justify their being placed in 
separate species. The sori of P. album are not only larger but are 
usually more numerous in a whorl, hence its fructifications are more 
conspicuous ; moreover, the stalks of this species are rather constantly 
weak at the base, so that the fructifications lie close to the substratum 
in a characteristic fashion. 

CCENONIA Van Tieghem (1884). 

Sorus globular, borne at the summit of a stalk which is dilated into a 
sort of cupule, in which the sorus is supported. 

Ccenonia denticulata Van Tieghem. 
Bull, de la Soc. Bot. de France, XXXI. p. 303-300. 1884. 

Sorus yellowish; stalk colorless, 2-3 mm. high, having a dilated 
base and expanding at the summit into a cupule which is finely toothed 
at its edges ; each peripheral cell of the stalk bearing a tooth or papilla 
on its exposed side. Spores Q^-S/j. in diameter, with yellowish cell 

On decaying beans. France. 

This remarkable form, so far as I am aware, has not been met with 
since it was originally described by Van Tieghem. 


Organisms having two definitely recurring stages, — a vegetative stage 
in which spindle-shaped or rarely spherical amoebae, bearing usually 
bipolar filiform pseudopodia singly or in tufts, may be either isolated or 
combined by the union of the pseudopodia into colonies forming net-plas- 
modia; and a fructifying stage, in which aggregations of individuals, com- 
parable to pseudoplasmodia, form spores borne in stalked or sessile sori. 


Saprophytic or parasitic organisms living on dung, or on alga? in fresh 
or salt water. 

LABYRINTHULA Cienkowsky (1867). 

Amoeba? spindle-shaped, colorless, or colored by means of yellow fat 
bodies. Spores borne in formless masses, producing one to four amoeba? 
at germination. 

The species of this genus have thus far been observed only by the 
authors cited. 

Labyrinthula vitellina Cienkowsky. 
Archiv. f. mikros. Anat., III. p. 274, Taf. 15-17. 1867. 

Amoebae containing orange-red coloring matter, which turns blue with 
iodine. Spores oval or spherical, 12^ in diameter, producing four amoeba? 
at germination. 

Living on sea-weeds growing on piles in Odessa harbor, Russia. 

Labyrinthula macrocystis Cienk. 
Archiv. f. mikros. Anat., III. p. 274, Taf. 15-17. 1867. 

Colorless or feebly yellowish. Spores spindle-shaped, 18^-25^ long, 
imbedded in a hyaline substance ; the contents producing four amoeba? 
at germination. 

Living on alga? growing on piles at a higher elevation than L. vittelina, 
only submerged by the surf. Russia. 

Labyrinthula Cienkowskii Zopf. 
Beitriige zur Pliys. u. Morph. niederer Organismen, II. p. 36-48, Taf. IV, V. 1892. 

Sori colorless, naked. Spores at germination producing only one or 
at most two amoeba?. 

Living in fresh water, parasitic on Vaucheria. Germany. 

DIPLOPHRYS Barker (1868). 

Amoeba? spindle-shaped or nearly spherical, with yellowish oil globules. 
Fructification (in D. stercorea) a definite stalked or sessile sorus. 

Diplophrys Archeri Barker. 
Quart. Jour. Mic. ScL, VII. p. 123. 1868. 

Individuals nearly spherical or broadly elliptical, 4^-5^ in diameter, 
bearing at almost opposite poles a tuft of filiform pseudopodia ; the pro- 


toplasm containing an oil-like refractive globule of an orange or amber 
color. Fructification unknown. 

Living in fresh water. Ireland, Germany, Pennsylvania and New 
Jersey (Leidy). 

In this provisional arrangement, I have followed Cienkowsky in refer- 
ring this species to the Labyrinthulese, although I regard it as improbable 
whether Diplophrys Archeri and D. stercorea should be included in the 
same genus. The aggregations of the vegetating amcebce of D. Archeri 
seem to be an association of the young iu groups, the colonies being 
formed by successive division of the individuals ; and there is nothing 
definite known concerning a resting stage. 

Diplophrys stercorea Cienkowsky. 
Archiv. f. mikr. Anat, Bd. XII. p. 44. PI. VIII. 1876. 

Individuals lens- or spindle-shaped, about 4^-6^ long, bearing at both 
ends several pseudopodia, almost bilaterally symmetrical. In the interior 
a nucleus, one or two contractile vacuoles and a yellow pigment body. 
Both the isolated and united individuals of the net-plasmodium finally 
becoming aggregated to form without change of shape pseudospores borne 
in sori, which are usually stalked, sometimes sessile. 

On dung of horse, cow and porcupine. Russia; Cambridge, Mass.; 
Intervale, New Hampshire. 

This species has been met with twice in American cultures, and so 
far as I am aware, with the exception of D. Archeri, is the only repre- 
sentative of the Labyrinthuleae which has been found in this country. 

A form, which is probably the resting condition of Cldamydomyxa laby- 
rinthuloides Archer, has been found growing in the cells of sphagnum, 
at Kittery, Maine, by Professor Thaxter. As Archer and others have 
pointed out, however, it is very doubtful whether this peculiar organism 
should be included in the Labyrinthuleae. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 13. — January, 1902. 



By Theodore William Richards and Ebenezer Henry Archibald. 



By Theodore William Richards and Ebenezer Henry Archibald. 

Received November 23, 1901. Presented December 11, 1901. 


Long ago Miahle observed that a concentrated solution of common 
salt acts upon calomel with the formation of small amounts of mercuric 
chloride.* Many years afterwards, one of us,f without knowing of his 
work, rediscovered this reaction, and found that the fluctuations in the 
potential of the " normal calomel electrode " of Ostwald, are due to ita 
disturbing influence. At that time it was shown that the reaction is 
much diminished by dilution, and hence that a decinormal solution is far 
better as an electrolyte than a normal solution. The "decinormal 
electrode," thus recommended for the first time, has since come into 
common use. 

It was shown also that neither light nor oxygen are important causes 
in effecting the decomposition, but that the reaction is much furthered by 
increase of temperature. No attempt was made at the time to fathom 
the matter, but a suggestion was made that the reaction might be due to 
the catalytic action of the ionized chlorine of the dissolved chloride. 

The investigation of the problem which was at that time promised has 
now been continued, and the object of this paper is to show that while the 
second condition of this suggestion seems probable, the first does not hold. 
Another example is thus afforded of the frequently recurring circum- 
stance of the removal of a reaction from its classification among catalytic 
phenomena after better acquaintance with its nature. 

* Miahle, J. Pharm., 26, 108; Ann. Cliim. et Phys. (3), 5, 177 (1842). 
t Richards, These Proc, 33, 1 (1897) ; Z. phys. Ch., 24, 39. 


The method employed was to treat calomel with solutions of chlorides 
of various concentrations for varying times, and to determine the extent 
of the reaction by determining the amount of mercury dissolved. 

Preparation of Materials. 

Mercury already very pure was thoroughly freed from the possible 
presence of substances with greater solution-tension by treatment with 
sulphuric acid and potassic dichromate, and subsequent spraying through 
ten per cent nitric acid. Calomel was resublimed at as low a temperature 
as possible, and thoroughly washed with water and with the solution to 
be used in each particular case. One of us had previously shown that 
the source of the calomel is immaterial.* Sodic chloride was precipitated 
by pure hydrochloric acid from a saturated solution of the so-called 
" chemically pure " salt. It was then twice recrystallized from water, 
and thoroughly dried to drive off any possible traces of acid. Pure 
calcic nitrate was made by many recrystallizations ; this was converted 
into carbonate, and the carbonate converted again into chloride. Several 
recrystallizations freed this chloride from every trace of the nitrate or of 
ionized hydrogen. Baric chloride was crystallized first from a solution 
strongly acid with hydrochloric acid, and subsequently from aqueous 
solutions by precipitation with pure alcohol. It also was wholly neutral 
to methyl orange. Cadmic chloride was made by dissolving the pure 
metal in pure acid and recrystallizing twice. The salt was dried 
thoroughly in order to make certain of the absence of ionized hydrogen, 
which is less easily detected in this case. Hydrochloric acid itself was 
purified by redistillation, the purest acid of commerce serving as the 

Apparatus and Method of Analysis. 

It was necessary to digest the mixtures for long periods of time 
at a constant temperature. For this purpose they were placed in large 
test-tubes of sixty cubic centimeters capacity arranged to rotate tran- 
sit-fashion in an Ostwald thermostat after the manner suggested by 
Schroder. f In the case of the weaker solutions several of these tubefuls 
were used for each analysis, but with the stronger solutions fifty cubic 
centimeters sufficed. The tubes were corked with rubber stoppers 

* Richards, loc. cit. 

t Richards and Faber, Am. Ch. J., 21, 168 (1899). The thermometer used to 
register the temperature was of course suitably verified. 


which had previously been boiled with dilute alkali and scrupulously 
rubbed and washed. Into each tube was placed a large excess of 
calomel, about a decigram of mercury, and fifty cubic centimeters of one 
of the solutions of chlorides. 

After a slight shaking, the settled precipitate was always covered 
upon standing with a layer of gray partially reduced material, which 
settled more slowly and hence gave more opportunity for reduction. 
When the equilibrium was completed by prolonged shaking, this gray 
material was mixed evenly throughout, and no longer appeared on the 
surface of the precipitate. Thus the absence of a gray film on settling 
was a rough guide to the completion of the reaction. 

After five or six hours of agitation in the thermostat at 25.° ± 0.05° 
one of the tubes was opened, its contents filtered, and the dissolved mer- 
cury determined analytically. At intervals of an hour successive tubes 
were similarly treated, and after seven or eight hours no change was 
found in any case. Evidently a state of equilibrium is soon attained, 
and the reaction cannot be called catalytic. The values given below are 
of course the values corresponding to this maximum. 

In this paper no evidence is given concerning the size of the grains of 
calomel. Ostwald * has recently shown that this may be an important 
factor in determining the concentration of a saturated solution, and 
hence in fixing the basis of the present equilibrium. Concerning this 
point it need only be said that while the absolute extent of solubility 
may vary with the size of the grains, the relative results, upon which 
alone the conclusions of this paper are founded, are not affected. This is 
the case because the same preparation of calomel was used in every 
instance. Moreover, since the calomel was sublimed and since it is 
notoriously difficult to powder, the individual diameters could not have 
been very small, hence a value approximating that corresponding to a 
flat surface must have been obtained. 

A number of experiments indicated that the mercury salt thus dis- 
solved was in the mercuric rather than in the mercurous state. The 
visible deposition of mercury during the reaction is alone almost enough 
to prove this. Moreover, neither permanganate nor bichromate suffered 
more than the faintest trace of reduction upon addition to a solution 
which contained much dissolved mercury. The minute trace of decolor- 
ization which was observed was no greater than that produced by a solu- 
tion of mercurous chloride in pure water. On the other hand, small 

* Zeitschr. phys. Chem., 34, 495 (1900). 



amounts of stannous chloride gave plentiful white precipitates of 

In all cases except that of cadmium, the mercuric salt in solution was 
determined as sulphide. The black precipitate produced by hydrogen 
sulphide was collected on a Gooch crucible, washed with alcohol, carbon 
disulphide, and again with alcohol, and finally dried at 100°. Satis- 
factory agreement between parallel analyses, which were almost always 
made in duplicate, was obtained. In the tenth-normal solutions of sodic 
chloride the amount of mercuric chloride was too small to be collected, 
hence it was determined colorimetrically by comparison with known 
solutions of similar dilution. 

The following table explains itself. The last-column contains an arbi- 
trary ratio which is an index of the changing relationship between the 
amounts of mercuric chloride formed and the amounts of sodic chloride 
present. The values in the third column were calculated from those in 
the second ; and the values in the fifth column from those in the third 
and fourth. 

Mercuric Chloride found in Solutions of Sodic Chloride. 

No. of 

( a 

S a 

Wt. of 








Wt. of 













Wt. of 
HgCI., in 
1 Litre of 


Mean Wt. 
of HgClj 

1 Litre. 








Cone, of 



in Equiv. 








1000 - c 


Hg<Jl 2 for 

every Mol. 









These facts, together with similar facts concerning solutions of three 
other chlorides, are represented in the accompanying diagram. Evidently 
the first parts of the four curves are very similar in tendency, but as the 
highest concentrations are reached, the curves develop individuality. 

Mercuric Chloride foond in various Solutions. 

The ordinates represent equivalent concentrations of the solvent chlorides, and 
the abscissae represent grams of mercuric chloride per litre of solution. The data 
for baric, calcic, and hydric chlorides are to be found on pages 352, 353, and 354. 

Manifestly some particular property of the several solutions must be 
responsible for the reaction ; and since the reaction results in raising the 
quanti valence of the mercury, it may be concluded that the particular 
property in question is the tendency of some molecular species already 
in the solution to combine with mercuric chloride. 



This conclusion concerning the action of the substances on mercurous 
chloride is reinforced by the facts concerning the extent to which mer- 
curic chloride is dissolved by solutions of various chlorides. Solutions of 
sodic chloride dissolve amounts of mercuric chloride which increase with 
the amounts of common salt present, until the saturation point is reached, 
while solutions of hydrochloric acid dissolve a maximum of mercuric 
chloride at a concentration of acid of seven times normal, remaining 
almost constant in action upon further concentration.* 

The parallelism between the tendency of these soluble chlorides to dis- 
solve mercuric chloride on the one hand, and their tendency to decompose 
mercurous chloride on the other hand, is thus rather striking. 

In addition to the four chlorides given iu the tables, cadmic chloride 
was used iu a special series of experiments. The solution after digestion 
with calomel was analyzed by immersing in it a roll of clean copper 
gauze, which was dried and weighed, and then ignited in hydrogen and 
weighed again. Preliminary experiments showed this to be a convenient 
and sufficiently accurate method of determining mercury in the presence 
of cadmium. 

Although solutions of 2, 4, and 8 times normal were used, in no case 

Mercuric Chloride found in Solutions of Baric Chloride. 

No. of 




Wt. of 








c. c. 





wt. of 


m. g. 



wt. of 
HgOl, in 
1 Litre of 


Mean Wt. 
of two Det. 
of UgCl 2 in 

1 Litre 







Cone, of 

BaCl 2 
iu Equiv. 







1000 ^, 


HgCI 2 for 

every J Mol 






* Homeyer and Ritsert, Pharm. Ztg., 33, 738, quoted by Comey, Diet, of Solubili- 
ties, 227 (1896). 

Ditte, Ann. Chim. phys., (5) 22, 551 ; Engel., ibid. (6), 17, 362. See Comey, as 


could a trace of mercury be detected in the solution. Moreover, no gray 
precipitate of reduced mercury was ever observed when the cadmium solu- 
tion was shaken with calomel in the first place. One infers that there 
is not in dissolved cadmic chloride any considerable concentration of a 
molecular species capable of combining with mercuric chloride. 

This conclusion is quite in accordance with the fact that the tempera- 
ture-coefficient of the potential of the calomel electrode with solutions of 
cadmic chloride exhibits none of the irregularities observed when other 
chlorides are used.* 

Mercuric Chloride found in Solutions of Calcic Chloride. 

No of 


1 b 





Wt. of 







Wt. of 


c. c. 

m. g. 





























Wt. of 
HgCl 2 in 
1 Litre of 



0.082 ) 

0.079 ) 


0.118 S 

0.232 ) 

0.230 ) 

0.320 ) 

0.323 ) 

0.429 ) 

0.431 ) 

0.518 ) 

0.519 ) 


0.509 ) 

Mean Wt. 
from two 
in 1 Litre 










Cone, of 
CaOl, Solu- 
tion in 
Q CaCl 2 ) 










1000 j, 


HgCl 2 for 

every h Mol. 










* llioliards, These Proceedings, 33, 1 (1897). 
vol. xxxvii. — 23 



Interpretation of Results. 

There are two possible interpretations of the phenomena under discus- 
sion. According to one, the undissociated mercuric chloride may be 
supposed to combine with the undissociated part of the electrolyte, 
forming an undissociated double salt, while according to the other, the 
undissociated mercuric chloride may be supposed to combine with the 
chlorine ion to form a complex ion. The following considerations at- 
tempt to decide which of these is more probable. 

Mercuric Chloride found in Solutions of Hydrochloric Acid. 

No. of 




Wt. of 




















Wt. of 


m. g. 


Wt. of 
HgCU in 
1 Litre of 

( 0.034 

( 0.034 ' 

C 0.048 ( 

} 0.048 ! 

0.206 : 

0.208 j 

0.400 j 

0.398 i 

0.548 ) 

0.548 ) 

0.653 ) 

0.655 j 

0.676 ) 

0.673 ) 





c C 

Mean Wt. Cone, of 

ofHgCl 2 I HC1 

in 1 Litre Solution 

of i in Equiv. 

Solution. Grams. 



















0.548 5.48 100.0 



HgCi, for 

every Mol. 











The shape of the first section of the curves, where the concentration of 
the mercury present increases at a greater rate than does the correspond- 
ing amount of electrolyte, suggests at first that the undissociated part of 
the latter is the portion concerned in the reaction ; but the curve repre- 
senting a power of the concentration of the ionized chlorine has of course 
a similar tendency. 

Hence the general shape of the curve is an insufficient basis for de- 
cision between the two hypotheses. 

The fact that strong solutions of cadmic chloride have little or no 
influence on mercurous chloride supports the latter of the two hypotheses, 
since concentrated cadmic chloride solutions contain but a very small 
concentration of ionized chlorine. 

More direct light upon the question is obtained by the measurement 
of electrolytic conductivity. According to the first hypothesis, which 
demands the presence of an undissociated double salt, the conductivity of 
salt solution should be considerably decreased by the addition of mercuric 
chloride. As a matter of fact, we found that the dissolving of mercuric 
chloride to saturation in a twice normal solution of common salt dimin- 
ished but slightly the conductivity of the solution. The work of Le Blanc 
and Noyes* furnishes similar results concerning hydrochloric acid; and 
moreover these investigators showed by the catalysis of methyl acetate 
that the concentration of the hydrogen ion was undiminished by the addi- 
tion of mercuric chloride. Hence the new compound is to be considered 
as highly ionized. 

Yet further evidence is to be obtained by referring to the specific con- 
ductivities of strong solutions of the chlorides studied. f Here we find 
that while the conductivities of solutions of sodic and baric chlorides 
increase with the concentration as far as they may be followed, those of 
calcic and hydric chlorides exhibit maxima at a concentration about six 
times normal. The agreement between these maxima and those ex- 
hibited by our own curves at seven times normal is close enough to 
suggest an essential relation between the cause of conductivity and the 
cause of Miahle's reaction. 

The evidence thus furnished is all consistent in indicating that the 
nature of the reaction is the addition of HgCL to the chlorine ion, with 
the formation of a complex ion. This conclusion agrees with that of Le 
Blanc and Noyes, based upon other data. 

* Le Blanc and Noyes, Zeitschr. phys. Chem., 6, 389, seq. (1890). 

t See Kohlrauseh and Holborn (1898), Leitvermogen d . Eleetrol., pp. 145-154. 


It remains now to detect the mechanism of the reaction. The work 
of Le Blanc and Noyes led them to believe that in dilute solutions con- 
taining an excess of the soluble electrolyte the new ion is bivalent, being 
formed by the reaction 2 CI' + HgCL = HgCl/'. It will be shown that 
our own evidence supports this conclusion also. 

The reaction with which we are concerned may perhajis be written 
thus : — 

xHCl ±; xH- + xCl' 

Hg 2 Cl 2 *; HgCl 2 + Hg 

•fl +1 ♦ I 

1+ 1+ I * 

Solid Hg 2 Cl 2 HgCl, 2 i x \ Liquid mercury 

The ion HgCl (2+I) will of course be the bearer of x negative charges of 
electricity. The above expression does not attempt completeness, but 
strives merely to represent the most essential features of the reaction in 
the simplest possible form. 

The first conclusion to be noted is that the concentration of the un- 
combined but dissolved mercuric chloride will be constant, since it is 
formed by a reaction involving two precipitates. Hence the concentra- 
tion of the ion HgC\ i2+%] should vary as the concentration of the chlorine 
ion raised to the x(h power. 

It is immediately clear that x must be more than unity, for in the less 
concentrated solutions the concentration of the mercury present increases 
faster than that of the dissolving chloride, while the concentration of the 
ionized chlorine is supposed to increase less rapidly than the latter. 

By taking x = 2 we obtain much more satisfactory agreement. If we 
assume that the concentration of the ions present is proportional to the 
specific conductivity,* we find that for solutions as far as twice normal the 
calculated curve agrees almost precisely with the actual amounts of mer- 
cury found. The specific conductivity of a twice normal solution of 
hydrochloric acid is 0.505, while that of a normal solution is 0.295. 
The squares of these numbers are respectively 0.255 and 0.087, two 
values which are very nearly proportional to the weights 148 and 48 
milligrams of mercury per litre which were actually found to be dis- 
solved from calomel by twice normal and by normal solutions of hydro- 
chloric acid respectively. 

With more concentrated solutions the results of this calculation agree 

* The possible dangers of this assumption are well known. It is made here 
simply in default of more certain knowledge. 


less and less satisfactorily with the facts, the amount of mercury actually 
found always exceeding the calculated amount. Evidently this disagree- 
ment may be due to the fact that some of the new complex acid remains 
in the uudissociated state; the calculation considers only the ion, while 
the mercury weighed in analysis constituted the sum total. The exact 
calculation of the amount undissociated is impossible for two reasons; 
in the first place, the mode of dissociation of such a tri-ionic comjxmnd as 
H 2 HgCl 4 is uncertain ; and in the next place, we have no data for the 
extent of the dissociation of the compound beyond the strength of a nor- 
mal solution. • 

In spite of this double uncertainty, it is possible to make an approxi- 
mate calculation. This is sufficient to show that in a general way the 
argument is sound. The approximate calculation is based upon the fact 
that so far as the extent of dissociation of the complex acid is known, it 
is equal to that of hydrochloric acid at the same concentration.* On mak- 
ing the assumption that this relation holds in very strong as well as in 
moderately strong solutions, and waiving entirely the uncertainty as to the 
possible existence of the half-way ion HHgCl 4 ', the proportion of the 

Approximate Calculation of the Total Amount of Mercury. 

tion of 
Acid Solution 
or Qrani- 
Equiv. per 

K = specific 

Conductivity of 


Acid a\t 

K 2 . 

a = • 


385 if- 



found in 

1 Litre 

Solution. % 

















































* Le Blanc and Noyes, loc. cit. 

t These figures were obtained by graphic interpolation from the figures of 
Kohlrausch and Holborn, Leitvermogen U. Eiectrol., p. 154 (1898). 
\ By interpolation. 


undissociated complex may be calculated by simply multiplying the sup- 
posed concentration C of the ionized part of the complex by , when 


a is the degree of dissociation of the acid. The total concentration of the 

-i ri 

mercury present would then be C -f- C = -. But if the new 

ion has the formula HgCl 4 ", its concentration should be proportional to 

the square of the specific conductivity, k, according to our previous 

C k 2 

reasoning. That is to say, — =k — .* This equation is tested in the 

a a 

following table, by taking a value for the constant k which best satisfies 

the early part of the curve — namely 385. 

The bearing of these rather discrepant figures is best seen by plotting 

the results. The curve which depicts the relation of the quantity 

385 k 2 
to the concentration of the hydrochloric acid is indicated by a 

dotted line in the diagram on page 351. While with great concentrations 
it deviates considerably from the curve representing the amount of 
mercuric chloride formed by hydrochloric acid, it is nevertheless of the 
same general character. Considering the many uncertainties, including 

the doubt concerning the equation a = — , which interfere with its exact 


determination, the agreement is indeed as close as one has a right to 

Corresponding curves, with about the same degree of agreement, may 
be calculated for the other chlorides. It is perhaps worth while to call 
attention to the fact that the amount of mercury found in the most dilute 
solution studied, the tenth normal solution of sodic chloride, although very 
small, is too great to correspond to the theoretical value. The excess of 
about three milligrams per litre above the requirement of theory may 
well be due to dissolved calomel, which possesses a slight but unknown 
solubility of its own.f 

All these arguments, reinforcing the conclusions which Le Blanc and 
Noyes reached from a different series of facts, seem to indicate that as 

*k — = k f - Tr because a = and k' = kA aa . Tlie more complex form is 

o \ A x 

retained because its meaning is the more obvious. 

t The work of Kohlrausch and Rose (Zeitschr. pliys. Cliem. 12, 241) is not con- 
clusive concerning this solubility, since the behavior of calomel on solution is too 
little known. Their results seemed to indicate that the solubility amounted to 
three or four milligrams per litre. 


nearly as the present means can determine, the reaction which we have 
been studying is to be thus represented in its simplest form : — 

Hg 2 Cl 2 + 2C1' = Hg + HgCl 4 ". 

It is of interest to classify the equilibrium under consideration accord- 
ing to the Phase Rule of Willard Gibbs. Looked at from this point of 
view, we may speak of the system as consisting of four components, — 
water, soluble salt, mercury, and mercuric chloride. It is clear, therefore, 
that when we have together the four phases, — mercury, mercurous 
chloride, solution, and vapor, — at a fixed temperature, a single condition 
of freedom remains to be fixed in order to fix the system. The concen- 
tration of the ionized chlorine seems to supply this sixth (n + 2d) con- 
dition, determining the fixed points in the tables. 

At the seven times normal point the concentration of the mercury dis- 
solved seems to attain almost a constancy, being no longer increased by 
further addition of soluble electrolyte. According to the Phase Rule, 
such a phenomenon might be caused by the appearance of a new phase. 
This new phase would of course be one which would remove hydro- 
chloric acid from the solution - } hence its presence or absence is easily 

As a matter of fact, we found that after continued shaking with 
calomel, hydrochloric acid having an original concentration of 9.22 
normal was reduced only to 9.20 normal. This is quite too small a 
difference to be due to the formation of a new phase ; it must be ascribed 
either to adsorption by the calomel or to analytical error. 

Hence the constancy of mercury dissolved is to be ascribed to con- 
ditions within the solution, and not to the appearance of a new 

Since the reaction seems to be effected primarily by the action of the 
chloride ion, it might be used to determine the concentration of the 
chloride ion, — or in the corresponding cases, that of the bromide or 
iodide ion. Especially would the case be applicable to the ionized 
chlorine because here the amount of mercury dissolved is too small to 
affect seriously other equilibria existing in the solution. Of course, with 
very dilute solutions the solubility of mercurous chloride itself would 
have to be taken into account. 

This tendency of mercuric chloride to add to the chloride ion is 
a highly interesting circumstance. Other similar phenomena are being 
more and more frequently reported.* The tendency of cadmium to form 

* Cushman, Zeitschr. fur anal. Chem., 34, 3G8 (1895). 


a similar complex ion is well known ; it has even been used by Cushman 
under Sanger's direction as a means of separating cadmium from other 
metals. In this case the complex ion was formed simply by adding an 
excess of sodic chloride, which prevents cadmium from being precipitated 
by hydrogen sulphide. Upon dilution the sulphide of cadmium hegins to 
be precipitated, owing to the splitting apart of the ion in dilute solutions 
according to the law of " mass " action. 

The same tendency has been used to explain the otherwise incom- 
prehensible migration values of cadmium salts. Very recently Noyes has 
shown that probably a similar ion, BaCl/',* exists in baric chloride so- 
lutions ; and the migration values of concentrated calcic and magnesic 
chloride solutions lead one to infer that in these cases yet a greater 
concentration of CaC'l 4 " and MgCl/' may exist. 

It is interesting to note that the decomposition of the mercurous 
halide is carried to a much greater extent under similar conditions in the 
case of the bromide than in that of the chloride,f and yet further in 
the case of the iodide. This may be due simply to the greater solubilities 
of mercurous bromide and iodide, but besides this cause there may exist 
a greater affinity of the molecule for the ion. The study of the migra- 
tion values of cadmium salts seems to show that the iodide has a much 
greater tendency to add to ionized iodine than the chloride has to add to 
ionized chlorine ; and it is probable that the same relation exists in the 
case of mercury. 

The facts recorded above show that an accurate quantitative analysis 
of a mercurous salt by precipitation with a soluble chloride is not to be 
expected, unless the chloride is added only in very slight excess, and 
then the solubility of mercurous chloride itself must be considered. 
When, however, a large excess of mercuric salt is present, as for example 
in the recent work of Ogg,} it is obvious that the disturbing effect of the 
side-reaction must be much hindered, according to the law of " mass " 

It is possible that the medicinal action of calomel is due to the small 
but definite concentration of mercuric complex salt produced by common 
salt or hydrochloric acid in the alimentary canal. In any case, one is 
disposed to recommend cautious medicinal use of other chlorides in con- 
nection with calomel. 

Preliminary experiments with sulphates showed that with these salts 

* A. A. Noyes, J. Am. Chem. Soc, 23, 37-57 (1901). 

t Richards, loc. cit. 

t Ogg, Zeitschr. phys. Chem., 27, 291 (1898). 


the tendency to form complex compounds is much less than that 
exhibited by chlorides ; hence the Latimer-Clarke and Weston cells are 
not much affected by this type of side-reaction. 

The results of the present paper may be stated briefly as follows : — 

1. The action of dissolved chlorides upon calomel is not catalytic, but 
results in the establishment of a definite equilibrium. 

2. With equivalent solutions, less concentrated than five times nor- 
mal, hydrochloric acid and sodic chloride have about equal tendencies to 
effect the reaction ; baric chloride has less tendency, calcic chloride still 
less, and cadmic chloride no appreciable tendency. 

3. The extent of the reaction in solutions not too concentrated is 
approximately a simple function of the square of the concentration of the 
chloride ion. This relation, taken in connection with a number of other 
considerations, points to the existence of a highly ionized complex 
HgCl/' in the solution, and thus confirms the work of Le Blanc and 

4. If approximate allowance is made for the probable concentration of 
undissociated complex salt present, all the figures, even as far as ten 
times normal solutions, seem to be explicable. 

5. The suggestion is made that the reaction may be of use as a 
means of determining the concentration of the chlorine ion. 

6. The corresponding reactions are much less marked with sulphates, 
but much more so with bromides and iodides. 

7. Caution is needed when using mercurous chloride as a means of 
determining mercury in quantitative analysis. 

Cambridge, 1899-1901. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 14. — February, 1902. 




By Theodore William Richards and Benjamin Shores Merigold. 



By Theodore William Richards and Benjamin Shores Merigold. 

Presented December 11, 1901. Received December 19, 1901. 


Our knowledge of uranium dates from the year 1789, when it was first 
recognized as an element by Klaproth. It can by no means, therefore, 
be classed with the new elements, nor is it of great rarity. Nevertheless, 
comparatively few determinations of the atomic weight of this element 
have been made, and of these, one only has been carried out with the 
degree of accuracy necessary in work of this kind. During the fifty 
years following the discovery of uranium a number of atomic weight 
determinations were made by Berzelius, Arfvedson, Schonberg, Mar- 
chand, and Rammelsberg. This early work is now of historical interest 
only, for the results vary widely, and in some cases are of such a nature 
as scarcely to be considered quantitative, in the modern sense of the 
word. For example, Rammelsberg obtained results varying from 184 
to 234, calculated upon the modern basis. 

In 1841 Peligot discovered that the substance then known as uranium 
was not an element, but an oxide. This discovery, while it did not 
impair the value of the analytical work previously done, necessitated a 
recalculation of the numerical value of the atomic weight. The new 
value was 120, and this remained practically unchanged during the next 
thirty years. When the periodic classification of the elements was first 
suggested, uranium, with the atomic weight 120, was one of the elements 
for which there was no place. From a study of the properties of 
uranium and its compounds, Mendeleeff declared that the atomic weight 

* The greater part of the work described in this paper was presented to the 
Faculty of Arts and Sciences of Harvard University by B. S. Merigold, as a thesis 
for the degree of Ph.D., in June, 1901. 


of uranium was probably 240 instead of 120.* The question was not 
definitely settled until Zimmermann, in 1885, carried out the suggestions 
of Mendel eeff, and by specific heat and vapor density determinations 
confirmed the higher value.f 

Owing to the wide variations in the published results, the atomic 
weight of uranium has long been considered one of the least satisfactorily 
determined of the atomic weight values. A glance at the results thus 
far obtained is sufficient to show the need for further work in this line. 
A complete resume of the older work upon the subject is to be found in 
Clarke's recent work on the atomic weights. | The following table 
summarizes those investigations which seem to possess even a little 
quantitative value: — 

Less Inaccurate Pkeviocs Work on the Atomic Weight of Uranium. 

O = 16.000 

1841 Peligot §— Analysis of Green Chloride 240. ± 

1842 Ebelmen || — Combustion of Oxalate 238. ± 

1843 Wertheim IT — Double Acetate of Sodium and Uranium 239. ± 
1846 Peligot** — Combustion of Oxalate and Acetate . . 240. ± 
1886 Zimmermann ft — Reduction of Oxide, U 3 8 to U0 2 . 239.6 
1886 Zimmermann $$ — Ignition of Double Acetate . . . 239.5 

The work of Ebelmen, "Wertheim, and the early work of Peligot is neces- 
sarily of little weight in assigning a probable value to the atomic weight 
of uranium. In some cases the material used was impure, and in others 
the methods of analysis were faulty. Consequently it is not surprising 
to find differences of whole units in the individual determinations of 
each series. 

Peligot's later determinations from the oxalate is perhaps the best of 
the early work. His material was carefully purified, and his method is 
far preferable to the work of Ebelmen and Wertheim. By combustion 

* Annalen der Cliemie u. Pharmacie, Supp. Vol. 8, 178 et. seq. 
t Annalen der Chemie u. Pharmacie, 216, 1. 

J A Recalculation of the Atomic Weights, by F. W. Clarke, Smithson. Misc. 
Coll., Constants of Nature, Part V. (1897), 263. 

§ Compt. Rend. 12, 735. Ann. Chim. Phys. (3) 5, 5 (1842). 

|| J. prkt. Chem. 27, 385 (1842). 

1 Ibid., 29, 209 (1843). 

** Compt. Rend., 22, 487 (1846). 

tt Ann. d. Chem., 232, 299 (1886). 

U Ibid. 


analysis he determined the ratio between uranium oxide and carbon 
dioxide. Thus he eliminated the error involved in weighing a crystal- 
lized salt which would probably contain more or less included water. 
The principal sources of error are the questionable use of combustion 
analysis in atomic weight investigations, and the possibility of unoxidized 
carbon remaining in the uranium oxide. His best results vary from 
239.4 to 241.1. 

The work of these chemists, though a great improvement over the 
attempts of Rammelsberg and the other early workers, leaves much to 
be desired, and does little more than give an approximate idea of the 
probable value of the atomic weight of uranium. 

Zimmermann's investigation of the ratio between the oxides UO.. and 
U 3 8 was much more carefully carried out, and is the only work thus far 
published that is worthy of serious consideration. Using carefully purified 
material, and giving attention to detail, Zimmermann oxidized the lower 
oxide by means of a stream of oxygen, and observed the gain in 
weight. His results for the atomic weight varied from 239.49 to 
239.76, an extreme difference of 0.27, or 0.11 per cent. The average 
was about 239. G. The chief probable cause of error in this method is 
the difficulty which is always experienced in forming a more voluminous 
solid from a less voluminous one. Uranous oxide has a specific gravity 
of 10.2, while the " Uranoso-uranic " oxide has a specific gravity of 
only 7.3. The great increase of volume which occurs when the higher 
oxide is formed must tend to protect particles of the lower oxide from 
the action of the oxygen. Hence the gain in weight will be too small, 
and the apparent atomic weight of the metal too large.* It is clear 
that a very small deficiency in the weight of the higher oxide must 
cause a great increase in the apparent atomic weight. 

Moreover, any incompleteness in the reduction by which the lower 
oxide was prepared, or any retention or occlusion of gases within this 
oxide, would also tend to raise the apparent atomic weight. Hence one 
is inclined to believe, even without further evidence, that Zimmermann's 
result for uranium must be too high. 

A new determination of the atomic weight of uranium has recently 
been made by J. Aloy.f The method employed differs materially from 
any previously used in uranium work. The values obtained are derived 

* Compare Richards and Baxter, These Proceedings 34, 351 (1898). Ztsch. 
anorg. Chem. 21, 251 (1890). 

t Comptes Rendus, 132, 551 (1901). This work is discussed rather fully here, 
since it is too recent to have been included in Clarke's book. 



from the ratio between the weight of nitrogen and that of uranous oxide 
contained in crystallized uranyl nitrate. Uranyl nitrate was purified by 
repeated crystallization. A quantity of the pure nitrate, the weight of 
which need not be known, was put iuto a boat, and the boat surrounded 
by a section of platinum tube, to prevent loss of material. The whole 
was placed in a combustion tube between spirals of reduced copper. 
One end of the combustion tube was connected with a carbon dioxide 
generator, and the other with an absorption apparatus containing a con- 
centrated solution of potash. 

After sweeping the air out of the apparatus with a current of carbon 
dioxide, the nitrate was heated so long as evolution of nitrogen occurred, 
the temperature being finally raised to red heat. The reduced copper 
was kept at red heat throughout the operation. When it was certain 
that no more nitrogen was evolved, the green oxide remaining in the 
boat was reduced by hydrogen to uranous oxide and weighed. The 
nitrogen was transferred to a measuring tube reading to tenths of a 
cubic centimeter. From the ratio of the weight of this volume of 
nitrogen to the weight of the oxide, the atomic weight is calculated. 

The following are the results of the eight determinations given : — 

Atomic Weight of Uranium. 
N = 14.04 

Volume of nitrogen, 15.25 cc. 
Atomic wt. of uranium, 239.3 









This method has the merit of simplicity, and does not involve the 
weight of the crystallized salt. There are, however, several sources of 
possible constant error that have not been taken into account. When 
crystallized uranium nitrate is heated, it first melts in its water of crystal- 
lization. As in all similar cases, it requires the very greatest care to 
prevent spattering while the crystal water is being driven off. It was 
undoubtedly as a precaution against loss of material in this way that 
Aloy used his platinum tube. By the time the crystal water is expelled, 
the fused mass has hardened into a solid cake, changing in color from 
yellow to orange, and finally to the green of urano-uranic oxide, U 3 8 . 

This method of preparing the green oxide from pure uranyl nitrate 


was used in the work to be described in the following pages. It was 
invariably found, however, that during the decomposition of the dried 
nitrate, and the subsequent oxidation, the oxide first produced forms a 
protecting crust, as it were. This prevents, or at least very materially 
retards, the decomposition of the material within the interior, even when 
the temperature is maintained for several hours at red heat. On the 
outside, the material had the appearance of being completely converted 
to oxide. On powdering the lumps, however, and again heating, there 
was in every case a further evolution of nitric fumes. Moreover, nitrogen 
itself is often retained by oxides prepared in this way.* It seems thus 
extremely probable that the quantities of nitrogen measured by Aloy 
were in every case too small. Obviously, until this point is definitely 
settled, Aloy's results must be regarded with more or less suspicion. 

It has been pointed out that reduction is usually much more complete 
than oxidation. f During the reduction of an oxide, there is formed, 
jierhaps, by the removal of a portion of the oxygen, a kind of skeleton 
framework, giving to the remaining substance a porous structure which 
enables the reducing gas to penetrate farther into the interior of the 
mass, until reduction is complete. Owing to this action, it is probable 
that when the green oxide of uranium is finally reduced by hydrogen, 
all the nitrogen is expelled, and the final product is pure uranous oxide. 
Consequently, the weight of uranous oxide used in the calculation is 
probably nearly correct, the principal error being in the volume of 

Aside from this special objection to the use of this method in its 
application to uranium, there is the general objection to the use of such 
a method where great accuracy is desired. The exact measurement of 
small quantities of gas offers considerable opportunity for error, especially, 
when, as in this case, the gas is first to be transferred from the collect- 
ing to the measuring apparatus. When the volume or weight of a gas 
is involved in an atomic weight investigation, it is customary to work 
with as large volumes as possible, thus reducing to a minimum the 
effect of the errors inevitably connected with the measurement of the 
gas. The exact measurement of a volume no larger than 165 cubic 
centimeters, even, — the largest volume measured by Aloy, — is a 
matter of considerable experimental difficulty, while with the smaller 
volumes, 15, 33, and 38 cubic centimeters, errors of at least 0.1% are 

* Richards and Rogers, These Proceedings, 28, 200 (1893) ; also Richards, 
Ibid. 33, 399 (1898). 

t Richards and Baxter, loc. cit. 
vol. xxxvn. — 24 


not only possible, but extremely probable. A difference of one tenth of 
one per cent in the volume of nitrogen makes a difference of 0.3 in the 
value of the atomic weight. The errors of collection and transference 
of the gas are more likely to result in reading too small rather than too 
large volumes, giving too high values for the atomic weight. 

From these considerations, it is evident that Aloy's results are at least 
somewhat doubtful. Aloy gives notice of his intention to apply this 
method to the determination of other atomic weights, but it is to be 
hoped that before doing so he will clear up some of the doubtful points 
in connection with the process. As carried out in this investigation, the 
method certainly is not a valuable addition to the methods of atomic 
weight determination. 

From the earlier results Clarke computed the value 239.6, while the 
German Committee recommend 239.5. Both figures are practically 
identical with Zimmermann's figures. 

The investigation herein described was undertaken with the hope that 
by increasing the experimental basis of our knowledge of the subject, we 
might be able to reduce to somewhat narrower limits our present uncer- 
tainty in regard to the real value of this constant. 

Preliminary Work upon the Preparation, Properties, and 
Methods of Analysis of Some Uranium Compounds. 

In view of the well known advantages of the halogen compounds for 
accurate analysis, when these compounds can be prepared and weighed 
iu a state of purity, — it seemed desirable to use a halogen compound as 
the basis of a determination of the atomic weight of uranium. 

Of the four chlorides of uranium known to exist, none can be pre- 
pared in a state of purity that is beyond question. Green uranous 
chloride, UC1 4 , which results from passing dry chlorine over a mixture 
of uranium oxide and carbon at red heat, is easily converted to the 
pentachloride, UC1 5 , by further action of chlorine at high temperatures. 
There can be no positive evidence that the green chloride would not 
contain some of the pentachloride, and if the attempt is made to prepare 
the pentachloride from the green chloride, it is equally difficult to be sure 
that the conversion is complete. The trichloride, UC1 3 , is made by reduc- 
ing the tetrachloride with hydrogen, and here again it is difficult to be 
sure that the tetrachloride is completely reduced. Uranyl chloride, 
UOoCL, cannot be prepared in the dry state. 

It is extremely probable, then, that any of the chlorides will contain 
larger or smaller quantities of a higher or lower chloride. It may be 


observed, in this connection, that Zimmermann used the chlorides in his 
vapor density determinations, and his analyses show good agreement. 
This does not show conclusively, however, that his material was free 
from small, but fairly constant quantities of higher or lower chlorides as 

On the other hand, bromine forms with uranium only three distinct 
compounds : the tribromide, UBr 3 ; uranous bromide, UBr 4 ; and the 
oxybromide, or uranyl compound, U0 2 I>i\>. The tribromide can be 
produced only from the tetrabrotnide by the action of reducing agents. 
Uranyl bromide, U0 2 Br 2 , has been certainly formed only in solution, 
resulting in hydrated crystals. It has never been definitely obtained in 
an-hydrous form. Zimmermann made many attempts to form the penta- 
bromide, corresponding to the pentachloride, by passing bromine at 
high temperatures over sublimed uranous bromide. Every attempt 
gave negative results, showing that at temperatures up to the subliming 
point of uranous bromide higher bromides cannot exist. Since higher 
bromides are non-existant under the conditions prevailing in the forma- 
tion of the tetrabromide, the objections to the use of the tetrachloride 
are not applicable in the case of uranous bromide. The investigations 
of Zimmermann* have shown that the tetrabromide can be formed in 
an apparently definite state. It seemed probable, therefore, from the 
literature on the subject, that in uranous bromide we had a conqjouud 
well suited to the purposes of our investigation. 

The method of preparation followed at first was essentially that 
described by Zimmermann.* In an apparatus constructed wholly of 
glass, a mixture of dry nitrogen and bromine vapor was passed over a 
mixture of the green oxide of uranium, U 3 8 , and pure carbon. The 
air was first thoroughly swept out of the apparatus by a current of 
nitrogen, and the oxide was heated to a high temperature. When the 
bromine vapor was passed in, uranous bromide formed, and sublimed in 
brilliant crystalline plates of a brownish color. After cooling in a 
current of nitrogen, the sublimate was transferred to a weighing bottle. 
At this point, however, unexpected difficulties arose, owing to the rapid 
oxidation of the bromide. Uranous bromide is extremely deliquescent, 
and forms with water and oxygen the oxybromide, with liberation of 
hydrobromic acid. Consequently, when exposed to the moist air of the 
laboratory even for the short time required for removing the sublimate 
from the combustion tube, the bromide loses its brilliant lustre, and 

* Annalen der Chemie, 216,3. 


assumes a dull, greenish yellow appearance, due to formation of the oxy- 
salt. If not protected from further action of moist air, the salt liquifies 
completely in a surprisingly short space of time. 

In an attempt to change the coating of oxybromide back to the 
normal salt, recourse was had to the method which has been used suc- 
cessfully in many atomic weight investigations carried on in this labora- 
tory. The salt was transferred to a platinum boat and placed, with a 
weighing bottle of suitable size, in a glass bottling apparatus* A 
stream of dry hydrobromic acid gas was then passed over the bromide at 
a temperature just below the subliming point of the salt. This treat- 
ment, however, fails to restore the original brilliant appearance of the 
freshly sublimed bromide. The yellow color of the oxybromide still 
remains. Apparently the oxybromide, once formed, cannot, by this 
method, be reduced to the normal uranous bromide. 

In the previous investigations upon zinc, magnesium, nickel, and 
cobalt, in which this method of converting oxy-salts to the normal com- 
pounds has been used, the presence of even minute quantities of oxy-salt 
was made known by the opalescence of the solutions on account of the 
insolubility of these salts. With uranium, however, this method of 
detecting the presence of uranyl bromide cannot be used, for the oxy- 
bromide of uranium is even more soluble than uranous bromide. 

The analysis of uranous bromide presents further difficulties. All 
uranous salts reduce silver nitrate. When a solution of silver nitrate, 
slightly in excess of the calculated amount, is added to a solution of 
uranous bromide, the silver bromide first precipitated is probably mixed 
with metallic silver; for if the silver bromide is filtered off, and the 
filtrate set aside, finely divided metallic silver soon separates. If a 
lar^e excess of silver nitrate is added to the uranous bromide, a brilliant 
purple precipitate is obtained. It is possible that the precipitate 
may be a mixture of finely divided metallic silver and argentic 
bromide, or perhaps of normal argentic bromide and the long sought 
sub-bromide. Although this is an interesting phenomenon, it was 
not considered advisable to interrupt the research at this period for 
the length of time necessary for an investigation. The addition of 
nitric acid prevents the formation of this colored precipitate, but owing 
to the danger of the loss of bromine, this is not an advisable expedient. 
Of course it is possible to determine the bromine by first precipitating 
the uranium and adding silver nitrate to the filtrate, but this introduces 

* For a description of this apparatus, see These Proceedings, 32, 59. 


a complexity of operations incompatible with the degree of accuracy 
requisite in an atomic weight investigation. 

On account of these formidable difficulties in the preparation and 
analysis of pure uranous bromide, it was thought best to search for some 
compound which offered fewer obstacles. Jt will be seen that this 
search was vain, although it required many mouths. 

In view of the great tendency of uranous bromide to oxidize, under 
ordinary conditions, the use of uranyl bromide seemed to offer the 
simplest solution of the problem. Anhydrous uranyl bromide has never 
been prepared in a pure state. In the preparation of uranous bromide, 
if the nitrogen used contains a little oxygen, or if traces of moisture are 
present, there is formed, in addition to the uranous bromide, a yellow 
powder, very different in appearance from the brown color of finely 
divided uranous bromide. This powder has been assumed by various 
investigators to be the oxybromide. Owing to the fact that it is always 
mixed with uranous bromide, an analysis has never been obtained. 

There seemed to be, however, some basis for belief that under suitable 
conditions of temperature, moisture, and oxygen supply, it might be 
possible to obtain anhydrous uranyl bromide entirely free from the 
uranous compound. With this end in view, the green oxide, without any 
admixture of carbon, was heated in a stream of bromine, also in a 
current of hydrobromic acid. In each case there was apparently no action 
whatever other than a partial and gradual reduction to the black oxide. 
This slight reduciug action is probably not due to the gases used, in the 
sense of being peculiar to them, for Zimmermann has shown that this 
reduction takes place whenever the green oxide is heated in a current of 
inactive gas such as nitrogen or carbon dioxide. * 

Both moist and dry gases were used. Mixtures of these gases and air 
were also tried, at different temperatures. The green oxide was then 
reduced by hydrogen to uranous oxide, U0 2 , and this was then treated 
with various combinations of dry and moist bromine vapor, hydrobromic 
acid, and air, at various temperatures. Again the results were negative. 
Under these conditions the bromine did not combine to the slightest 
extent with the uranium. Since combination fails to take place, even in 
the presence of considerable quantities of oxygen, there is naturally 
some cause to doubt that the light colored powder above mentioned is 
really an oxybromide. Possibly it is, after all, uranous bromide in a 
different state of aggregation. 

* Loc. cit. See also Eichards, These Proceedings, 33, 423 (1898). 


The hydrated uranyl bromide is more easily obtained. The green 
oxide was reduced by hydrogen to urauous oxide, suspended in water, 
and heated with bromine on the steam bath. After driving off the 
excess of bromine, uranyl bromide remains in solution. The solution 
may be evaporated to the consistency of a thick syrup, and even under 
the best conditions the yield of crystals is very small. Moreover, it is 
almost impossible to wash the crystals free from the mother liquor, 
since they are extremely soluble in water and alcohol, and ether decom- 
poses the compound, setting free bromine. Hence uranyl bromide was 

Of the iodine compounds of uranium, the iodate alone seemed promis- 
ing. This compound has been prepared and described by A. Ditte,* 
who assigns to it the anhydrous formula U0 2 (I0 3 ) 2 . The iodate was 
prepared by us as follows : — 

To a solution of uranyl nitrate, containing much nitric acid, was added 
a solution of iodic acid, prepared by warming finely powdered iodine 
with nitric acid of specific gravity 1.50. Both solutions were heated to 
boiling before mixing. Uranyl iodate is precipitated as a yellow, finely 
crystalline salt, but slightly soluble in water at ordinary temperatures. 
At 100°, however, if some nitric acid is added, it is possible to obtain 
a solution containing ten grams of iodate to the litre. On cooling, 
2.5 to 3.0 grams of iodate crystallize out. By recrystallizing a few 
times, in sufficiently large vessels, it is possible to obtain a compound in 
a high state of purity. 

The method of preparation described above is that recommended by 
Ditte. Although Ditte's course of procedure was carried out as ex- 
actly as possible, the compound obtained differed from that which he 
describes. Instead of being anhydrous, it contained one molecule of 
water. Inasmuch as Ditte's statement of the amount of nitric acid 
which he used is extremely vague, different concentrations were tried, 
from a solution slightly acid up to one containing twenty-five per cent of 
strong nitric acid. In every case the hydrated compound was obtained. 
Ditte did not recrystallize his compound, but our recrystallized product 
was identical with that which was only once precipitated. The analysis 
given is the average of ten concordant analyses of material prepared 
from both hot and cold solutions. Both recrystallized iodate and that 
precipitated only once are represented. The method of analysis is 
described below. 

* Annales de Chimie et de Physique, 6th Series, 21, 158 (1890). 


Analysis of Uranyl Iodate. 


Caleul:itril for 
U0 2 (I0 3 ),1IJ>. 

Uranous oxide 


42.34 % 

Iodic acid 



Water (by difference) 



100.00% 100.00% 

In determining the composition of the iodate, a weighed quantity of 
the substance was used, and the percentage composition by weight cal- 
culated in the usual manner. For an atomic weight determination, 
however, any method which involves the original weight of a salt 
crystallized from solution as a factor in the calculation must of course be 
avoided on account of the ever present possibility of included mother 
liquor. It was necessary, then, to determine directly the ratio of 
iodine to uranium, or to uranium oxide. To determine the uranium, 
advantage was taken of the behavior of the iodate on ignition. When 
heated, the iodate is decomposed, water, oxygen, and iodine being given 
off, leaving uranium oxide. The process was carried on in an ordinary 
combustion tube of hard glass, a current of dry air being passed through 
the tube. Since Zimmermann has shown that the green oxide under- 
goes partial reduction at high temperature unless in an atmosphere of 
oxygen, * a stream of oxygen was finally passed through the tube. The 
oxide was then cooled in an atmosphere of oxygen. Treated in this 
way, the decomposition of the iodate is not complete. Some iodine 
always remained in the oxide, even when the heat was maintained for 
three hours at a temperature just below the softening point of the com- 
bustion tube. To correct for this amount of iodine, the oxide was 
weighed, dissolved in dilute nitric acid, and the iodine precipitated as 
argentic iodide. The amount of iodine found in this way varied from 
0.1% to 1.0% of the total iodine, according to the duration of the period 
of ignition. 

Iodine was determined in another sample of material exactly similar 
to that used for the uranium. The method was, briefly, reduction of 
the iodate by sulphurous acid, and precipitation with silver nitrate. 
Stas has shown that silver iodate can be converted completely and with- 
out loss into silver iodide by the use of sulphurous acid,f and the same 

* Annalen der Chemie u. Pharmacie, 232, 287 (1886). 

t Untersuchungen iiber die Gesetze der chemischen Proportionen liber die 
Atomgewichte u. ihre gegenseitigen Verhaltnisse, J. S. Stas. Aronstein's transla- 
tion, p. 69. 


method applies equally well to uranium iodate. The iodate was sus- 
pended in 200 c.c. of water acidified with 20 c.c. sulphuric acid, cooled in 
ice to 0°, and pure sulphur dioxide was passed in until the solution 
smelled strongly of this reagent. The flask was then removed from the 
ice and shaken occasionally. From three to four hours is required 
before complete reduction takes place and the last traces of iodate go 
into solution. When completely reduced, silver nitrate is added, and 
heated to 60° in order to cause the more coherent deposition of the 
jjrecipitate.* Thus it was found possible to convert the" insoluble iodate 
into soluble iodide without loss of iodine. 

In this way the ratio of uranium oxide to iodine may be determined, 
regardless of the presence of occluded water in the iodate used, provided 
that the amount of water occluded be exactly the same in each of the 
samples. It would obviously be more satisfactory to determine both 
uranium and iodine in the same sample, provided a sufficiently simple 
method could be found. 

The following method was found to fulfil the required conditions 
fairly well. A quantity of the iodate was placed in a boat in a com- 
bustion tube, to one end of which was attached, by a ground glass joint, 
a weighed U-shaped tube. The free end of this tube was drawn out and 
fused to a smaller tube which dipped into a solution of sulphurous acid. 
On heating the iodate in a stream of air and oxygen, the salt was decom- 
posed and the iodine was carried over and condensed in the U-tube, 
which was packed in ice. The small quantity of iodine vapor not con- 
densed was collected in the sulphurous acid and precipitated as silver 
iodide. The heating: was contiuued for an hour after no more iodine 
could be seen coming off. The end of the U-tube was then sealed by 
fusing off the small tube, and the other end was closed by a ground glass 
stopper immediately after disconnecting from the combustion tube. In 
this way about ninety-nine per cent of the total iodine was weighed 
directly as free iodine. Of course the small amount of iodine remaining 
in the oxide after ignition had to be determined separately, as already 
described. By this method the amount of iodine found was practically 
identical with that found by the sulphurous acid method. 

In determining the iodine present in the oxide after ignition, it has 
been assumed that the iodine is present as iodide. Although it is hard 

* When silver iodide is precipitated in the presence of sulphurous acid, the 
supernatant liquid does not become clear enough to filter even after several days, 
unless heated to 60°. 

Vide Stas, " Untersuchungen," p. 69. 


to believe that at the temperature employed any of the iodine can exist 
as iodic acid, it is impossible to prove the point experimentally. The 
uncertainty in regard to this point renders the use of the method inadvis- 
able where the greatest possible accuracy is desired. Hence none of 
these analyses have any significance as a basis for computing the atomic 
weight of uranium. 

Besides the bright yellow, slightly soluble iodate, we prepared a paler 
yellow, more soluble, and more highly hydrated salt, which suffers transi- 
tion quickly into the earlier compound at a high temperature and more 
slowly at a low temperature. Double iodates with sodium and potas- 
sium were also prepared. Some of our observations were inconsistent 
with the published record concerning the subject ; but in spite of our 
desire to clear up the uncertainty and to study the rather interesting 
transition phenomena, we abandoned the iodates because none of them 
gave promise of a precise basis for the determination of the desired 
atomic weight. 

The next compound investigated was the oxalate, which has the com- 
position UO2C2CV 3H 2 0. Owing to the comparatively slight solubility 
of this compound it can be obtained in a state of great purity by a few 

The best method of analysis is that of dry combustion, the carbon 
dioxide being absorbed in potash in the usual manner. The uranium 
is left in the combustion tube as the green oxide, U 3 8 , and consequently 
can be compared directly with the weight of carbon dioxide obtained. This 
obviates the necessity of using the weight of the oxalate as a factor in 
the calculation of the atomic weight, and so eliminates the error due to 
included water. As already mentioned, this method has been used by 
Ebelrnen and Peligot in their determination of the atomic weight of ura- 
nium. There is in this method a possible source of error, difficult of 
detection and correction, but none the less dangerous, in the possibility 
that the uranium oxide may after combustion still retain traces of carbon. 
Moreover, it became evident, after a few analyses had been made, that 
combustion analysis, as ordinarily conducted, is an exceedingly question- 
able method where great accuracy is desired. The great difficulty in 
obtaining absolute "blanks "is well known. Our experience amply 
confirmed the observations of Mabery,* Auchy,t and others in regard to 

* Inaccuracies in the Determinations of Carbon and Hydrogen of Combustion, 
C. F. Mabery t Journal Am. Chera. Soc, 20, 510 (1898). 

t George Auchy, Journal Am. Chem. Society, 20, 243 (1898). 



the loss of water and possibly of carbon dioxide from the ordinary form 
of potash bulbs. We also found a single sulphuric acid tube entirely 
insufficient to absorb all the water. Clearly, then, if we were to use this 
method, an elaborate investigation of the form of apparatus, method of 
procedure, and limits of error, was absolutely imperative. The use of 
the oxalate, however, did not seem sufficiently promising to warrant the 
necessary expenditure of time. 

After thus investigating the uranium compounds which seemed likely 
to furnish a suitable basis for an atomic weight determination, anhydrous 
uranous bromide, in spite of its disadvantages, seemed most likely to fulfil 
the necessary requirements. As already mentioned, this confound oxi- 
dizes with the greatest ease on exposure to moist air. It was necessary, 
therefore, to devise apparatus which should preclude any possibility of 
bringing the sublimed bromide in contact with the air of the laboratory 
until it had been collected and weighed. After much experimenting 
with different forms of apparatus, the following method was adopted. 

Preparation and Collection of Puke Uranous Bromide. 

The mixture of urano-uranic oxide and carbon was placed in a porce- 
lain boat within the larger of two " telescoping " porcelain tubes. The 
portion of the tube containing the oxide was heated in a Fletcher furnace, 
and after thoroughly sweeping out the apparatus with dry nitrogen, a 
mixture of dry nitrogen and bromine vapor passed over the oxide. 
The sublimed bromide collected near the inner end of the smaller porce- 
lain tube. The very efficient and elaborate desiccating apparatus which 
served so well in the work on the atomic weights of cobalt and nickel, 
was very kindly given by Dr. Baxter for use in this investigation.* 
This apparatus , with slight modifications, was used for drying the nitro- 
gen and bromide, and was connected by a ground glass joint with the 
porcelain combustion tube. 

With this apparatus traces of air diffused through the annular joint 
between the porcelain tubes, forming a coating of oxide on the inner 
tube.f In the case of uranium, the oxide is found to be copiously mixed 
with the sublimate also. This diffusion of air takes place even when the 
outer end of the inner porcelain tube is nearly closed, thus making a 
considerable outward current within the tubes. 

* For a full description of this apparatus see There Proceedings, 33, 124 

+ In the case of cobalt and nickel this oxide was easily removed by subsequent 
treatment, but in the present case removal was impossible. 




In order to obviate the difficulty and exclude air a glass jacket was 
slipped over the joint between the tubes. The construction and use of 
this jacket will be made clear by reference to the accompanying drawing. 

Section of Subliming and Bottling Apparatus. 

A, outer porcelain tube fitted with ground glass joint B; C, inner porcelain tube 
with ground-glass stopper D ; E, boat containing oxide and carhon ; F, furnace ; 
G, glass jacket; H, H, H, H, packing of asbestos wool; I, weighing bottle; L, 
tube for admitting nitrogen, sliding within tube M through rubber connection N, 
and carrying at its end stopper of weighing bottle; P, sublimate; R, rod for 
removing sublimate. 

The jacket was drawn down at the ends, so as to fit the porcelain 
tubes A and C as well as possible, and the spaces between the tubes and 
the jacket were packed tightly with asbestos wool. This packing makes 
a joint sufficiently tight to withstand a pressure equal to that of eight or 
ten centimeters of water. The jacket was provided with a long tube, M, 
within which slid a second tube, L, connection being made by 'means of 
the short piece of rubber tubing, N. To the end of the inner tube was 
attached, by platinum wires, the stopper, O, of the weighing bottle. The 
outside diameter of L was very little less than the inside diameter of 
M, thus leaving very little space between the walls of the two tubes. 
For this reason, and also on account of the length of the tube M, — about 
fifteen centimeters, — there was little danger of bromine diffusing up in 
sufficient quantities to attack the rubber connection, N. Even if this 
were the case there could be no possibility of contamination of the sub- 


limate thereby, since there was always a constant outward pressure of 
bromine during the sublimation. The outer end of L was connected 
with the nitrogen supply of the desiccating apparatus. All glass joints 
and stop-cocks were lubricated with syrupy phosphoric acid. 

The method of procedure was as follows : In the porcelain boat, E, 
was placed an intimate mixture of urano-uranic oxide and pure carbon, 
the carbon being about twenty per cent of the weight of the mixture, 
thus insuring a large excess of carbon. The apparatus was then thor- 
oughly swept out by nitrogen, which enters at B and L simultaneously. 
After the air was completely expelled, the combustion tube was grad- 
ually raised to a high temperature by the blast lamp. Heating in a 
current of nitrogen was then continued for three hours at least, some- 
times longer, in order to insure complete removal of all traces of air and 
moisture. During this and subsequent operations, the outlet of the 
stopper D of the inner tube was nearly closed by asbestos wool, thus 
maintaining a constant and considerable pressure within the apparatus, 
and hindering the diffusion of air. After this preliminary heating in 
nitrogen, bromine vapor was passed in through B. During the first trials 
of the apparatus it was our practice to keep a slow current of nitrogen 
passing in at L during the sublimation. This kept the jacket entirely 
free of bromine, a very slow current of nitrogen being sufficient to keep 
any bromine from passing between the walls of the porcelain tubes. It 
was found, however, that traces of air diffused through the permeable 
asbestos packing, and were of course carried into the combustion tube by 
the current of nitrogen, forming on the inner tube a coating of oxide, 
and contaminating the sublimate. In order to avoid this, the nitrogen 
was shut off from L sometime before turning on the bromine. After 
turning on the bromine, the jacket slowly filled with dilute bromine 
vapor. While the greater part of the sublimate collected within the 
inner tube, a little collected between the walls of the two tubes, almost 
sealing the annular space. This sublimate, which collected on the outside 
of the inner tube, is a valuable indicator of the condition of the subli- 
mate within. In the presence of mere traces of oxygen the lustrous 
brown color of the uranous bromide gives place to a dull yellow color 
easily distinguishable. Comparatively small quantities of oxygen form a 
coating of black oxide. When the sublimation is conducted according to 
the method described, the outside of the inner tube is free from any traces 
of the supposed oxybromide or of oxide, thus showing that no appreciable 
quantity of moist air could have reached the innermost portions of the 
sublimate. The best proof of the purity of the sublimate is of course 


found in the agreement of analyses of substance formed under various 
conditions of bromine supply. 

After the bromine had been run for about one and a half hours, the 
sublimate was cooled for three hours in a current of nitrogen. When 
the tubes were thoroughly cold, nitrogen was finally passed into the 
jacket through L, in order to sweep out any traces of bromine that 
might still remain. The inner tube, containing the sublimate, was then 
carefully drawn out until the inner end reached a position over the 
mouth of the weighing bottle, indicated in the diagram by the dotted 
line. This can be done without seriously disturbing the asbestos pack- 
ing, a rapid current of perfectly dry nitrogen being admitted meanwhile 
through L. By means of the glass rod, R, the sublimate was pushed 
out of the tube and dropped into the weighing bottle, I. The tube 
L, carrying the stopper, was then pushed down and the stopper in- 
serted. The stopper was held by the platinum wires so lightly that 
after pushing it into place the tube L could be withdrawn, leaving the 
stopper inserted in the bottle. 

Thus uranous bromide was sublimed, collected, and bottled up in an 
atmosphere of dry nitrogen ready for weighing, without once coming 
in contact with the air of the laboratory. That the apparatus is effective 
for the purpose intended, and capable of producing material of constant 
composition, was shown by the first rough analyses of uranous bromide, 
which yielded 57.41, 57.41, and 57.42 per cent bromine respectively. 
These analyses were made with material that had not been purified, but 
served to show the constancy of composition of the sublimate ; for not only 
was the length of time occupied in the sublimation varied, but in one case 
the sublimate was cooled in bromine instead of in nitrogen. Of course if 
an appreciable amount of an oxygen compound were formed, by diffusion 
of air or moisture, there would almost certainly be discrepancies in the 
results, since it is hardly conceivable that under the varying conditions 
exactly the same quantities of oxy-salt should be formed each time. 

Because the specific gravity of uranous bromide was unknown, the fol- 
lowing determinations were made : 2.0328 grams of the salt displaced on 
one occasion 0.3332 gram of kerosene at 21°, and at another trial 0.3322 
gram. The kerosene had been redistilled, and only the high boiling 
portion was used. The density of the kerosene at 21°, referred to 
water at 4°, was 0.7919. Hence the specific gravity of the uranous 
bromide was (1) 4.830 and (2) 4.846, giving as the mean 4.838. 
This value was used in reducing the observed weights of bromide to 
the vacuum standard. 


During the weighing in the final analyses, the bromide of uranium 
was still surrounded by an atmosphere of pure dry nitrogen in the 
tightly stoppered weighing bottle. Since this bottle had been full of 
dry air when it was first weighed, a small correction had to be applied 
on this account. The difference in weight between 6.70 cubic centi- 
meters (the interior volume of the weighing bottle) of air and the same 
volume of nitrogen at 20° C. is 0. 0002(35 gram. Of this nitrogen a 

gram of urauous bromide displaced - - = 0.206 cubic centimeters, or 


0.24 milligram, while the brass weights used in weighing the bromide 
displaced 0.145 milligram of air. Hence in vacuum a gram of uranous 
bromide would weigh 0.265 + 0.24 — 0.145 = 0.36 milligram more 
than J the observed weight, while two grams would weigh 0.265 + 
2(0.24 — 0.145) = 0.46 more than the observed weight. All the weights 
given in the tables are corrected in this way to the vacuum standard. 

Methods of Analysis. 

By the use of these devices we were able to prepare and weigh pure 
uranous bromide in a definite state. There still remained, however, the 
problem of devising a suitable method of analysis. As previously men- 
tioned, all uranous compounds reduce silver nitrate, making impossible 
the usual method of procedure in halogen determinations. 

The method of precipitating the uranium and determining bromine in 
the filtrate involves too much danger of loss of material in the multiplic- 
ity of operations. The most satisfactory solution of the problem seemed 
to be to oxidize the compound to the uranyl salt, provided this could be 
done without loss of bromine. Nitric acid is of course effective as an 
oxidizing agent, but the oxidation is accompanied by loss of bromine. 
After much experimenting, hydrogen dioxide was found to be the most 
suitable oxidizer. From neutral solutions of uranium compounds, hydro- 
gen dioxide precipitates a hydrated peroxide of uranium. If the solution 
is slightly acid, this precipitation is prevented and the uranous compound 
completely oxidized to the uranyl state. The weighed sample of uranous 
bromide was dissolved in considerable water — at least 400 cubic centi- 
meters of water to each gram of bromide. The bottle containing the 
bromide was opened by means of a suitable glass fork, either below the 
water or just above the surface, so that it could be instantly submerged, 
and thus avoid loss of hydrobromic acid by the action of moist air. The 
calculated volume of a standard solution of pure hydrogen dioxide was 
then diluted to about 100 c.c, one cubic centimeter of pure dilute sul- 


pluiric acid was added, and the mixture was slowly run into the solution 
of uranous bromide. The screen color of the uranous salt soon changes to 
the yellow color characteristic of uranyl compounds. On adding the 
first few cubic centimeters of the dilute hydrogen dioxide solution, a 
greenish white precipitate came down. Addition of more of the acid 
dioxide solution redissolved it, and the resulting solution was perfectly 
clear. This peculiar hydrolytic action is due to the acid, and not to the 
hvdric dioxide, for the same reaction occurs if dilute sulphuric acid alone 
is added to the solution. 

The explanation of this interesting phenomenon, which is just the 
opposite of what might have been expected, is, undoubtedly, that the 
bromide is already hydrolyzed to a great extent by merely dissolving in 
water. The hydrate is probably in solution in the colloidal state. Evi- 
dence of this is found in the fact that if the clear aqueous solution of 
uranous bromide is allowed to stand exposed to the air, a hydrate gradu- 
ally separates, giving to the solution a cloudy, murky appearance. After 
two or three days this precipitate disappears, giving place to a clear 
yellow solution of oxybromide and hydrobromic acid. The addition of 
sulphuric acid coagulates the colloid before it can all be converted into 
uranyl salt. 

In order to be sure that no bromine or hydrobromic acid is lost by 
this method of oxidation, the following experiment was made. 0.5 gram 
of bromide was dissolved in 250 c.c. of water, 50 c.c. of dilute sulphuric 
acid (1 :10) was added, and the hydrogen dioxide solution was run in. 
This was done in a closed flask, similar in construction to a gas washing 
bottle. A current of air was drawn through the bottle and then through 
starch solution containing potassium iodide to see if bromine is liberated. 
Not the slightest trace of blue color appeared in the starch solution, even 
after adding a large excess of hydropen peroxide and allowing it to stand 
over night. A test for hydrobromic acid was sought in a similar way, 
by drawing the air through a solution of silver nitrate, again with nega- 
tive results, as was to have been expected. These experiments show 
conclusively that uranous bromide can be oxidized completely by hydro- 
gen dioxide, without loss of bromine. 

Silver nitrate, in moderately concentrated solutions, is not acted upon 
by a three per cent solution of hydrogen peroxide. Consequently a con- 
siderable excess of the latter reagent could do no harm. Nevertheless 
care was taken never to add more than the calculated amount of hydro- 
gen dioxide. Moreover, the solution of hydrogen dioxide used contained 
only one per cent of this reagent, and this was diluted ten times before 


adding to the bromide solution, thus reducing to a minimum the possi- 
bility of too vigorous oxidation, with consequent liberation of bromine. 

After the oxidation, bromine was precipitated by pure silver nitrate in 
the usual manner. This precipitation was conducted in an Erlenmeyer 
flask fitted with a ground glass stopper. The silver bromide was col- 
lected on a Gooch crucible, and dried in an electrically heated drying 
oven. Of course the asbestos shreds carried away in washing the silver 
bromide were collected by passing the filtrate and wash water through a 
fine filter, and their weight was added to that of the silver bromide. 
The bromine determination was carried on in orange colored light. 

It was found in the work upon cobalt and nickel that the porcelain 
tube is attacked by bromine vapor at the high temperature employed 
during the sublimation, with the result that sodium bromide was always 
present in the sublimate. In these investigations this impurity was de- 
termined by the reduction of the bromide to the spongy metallic state by 
means of hydrogen, and extraction by water.* A somewhat similar 
method was tried with uranium. Since hydrogen reduces uranous bro- 
mide only to the tri-bromide, the bromide was ignited in a current of air 
and the resulting oxide leached with water. It was found to be impos- 
sible to oxidize the bromide completely. A little uranous bromide 
invariably remained and was washed out with the alkali. Both dry and 
moist air was tried, also ignition in steam, but in every case uranium was 
washed out in considerable quantity. 

Precipitation of the uranium by hydrogen dioxide was next tried, but 
it was found impossible to precipitate the uranium completely. The 
rather unsatisfactory method of determining the sodium in the filtrate 
from the bromine precipitation, or in a new sample of uranous bromide 
as nearly similar as possible, after removing the uranium with ammo- 
nium sulphide, appeared to be the only available method. The filtrate 
and wash waters from the bromine precipitation were evaporated in 
platinum to small bulk, and the uranium and excess of silver precipitated 
by pure colorless ammonium sulphide. This reagent precipitates uranium 
completely. The filtrate was then evaporated to dryness, the ammonium 
salts expelled by ignition, and the residual sodic nitrate converted to the 
sulphate and weighed as such. Of course these operations were all con- 
ducted in platinum vessels. This method of work is not wholly satisfac- 
tory, on account of the complexity of operations involved, but it seems to 
be the only practical method. 

* These Proceedings, 34, 329, 359 (1899). 


Purification of Materials. 

As the source of uranium, commercial " chemically pure " uranium 
acetate was used.* This was first converted to the chloride on account of 
the greater solubility of this compound, — by precipitation as ammonium 
uranate and redissolving in dilute hydrochloric acid. To the hot and 
slightly acid solution, pure sulphuretted hydrogen was added to satura- 
tion. The free acid was then neutralized with amnionic hydroxide, a 
slight excess of the alkali was added, and more sulphuretted hydrogen 
was run in. In this way some uranyl sulphide was precipitated, in order 
to sweep down with it any colloidal sulphides of the higher groups which 
might otherwise escape removal. The excess of sulphuretted hydrogen 
was boiled off, and after standing over night the supernatant liquid was 
decanted through a washed filter. 

The next step depended upon the fact that uranium remains iu a 
solution of the double carbonate of ammonium and uranium, in the 
presence of an excess of ammonium sulphide, while all the other members 
of the aluminum and iron groups are thrown down by this reagent. 
Consequently amnionic hydrate and ammonium carbonate in slight excess 
were added to the filtrate, forming the double carbonate. If the solu- 
tions are concentrated, the double carbonate is precipitated when more 
than a slight excess of amnionic carbonate is used. This happened in 
some cases, when it was necessary to redissolve the precipitate in dilute 
hydrochloric acid and again add ammonic carbonate in more dilute 
solution. About fifty grams of carbonate per litre was found to give the 
best results. Ammonic hydroxide was then added to the hot solution, 
and sulphuretted hydrogen in excess. After stauding over night the 
solution was filtered. In several of the more concentrated solutions, a 
considerable quantity of the salt crystallized out. These crystals were 
worked up separately, as they were probably purer than the solution. 
On boiling the solution to decompose the excess of ammonium sulphide, 
some of the ammonic carbonate was decomposed, causing the precipita- 
tion of some uranium sulphide. This precipitate was discarded, as it 
might have contained iron, or other analogous metals which had previ- 
ously escaped precipitation. Dilute hydrochloric acid in slight excess 
was added, and the carbon dioxide was expelled by boiling. The free 
acid was then almost neutralized with pure ammonic hydroxide, and 

* This method of uranium purification, with some modifications and additions, 
is similar to that employed by Zimmermann. Annalen der Cliemie u. Pharmacie, 
232, 299. 

vol. xxxvn. — 25 


pure amnionic sulphhydrate added in excess. The color of the result- 
ing precipitate of uranium sulphide varies greatly with the temperature. 
In warm solution it was at first reddish brown, while that precipitated in 
the cold varied from bright red to brownish yellow. On washing, all 
turn black, the sulphide being decomposed into uranous oxide and sul- 
phur. After thorough washing the resulting mixture of oxide and 
sulphur was ignited in a porcelain dish, the green urano-uranic oxide 
being the product. 

The oxide was then dissolved in a platinum dish in redistilled nitric 
acid, evaporated, and recrystallized from nitric acid solution. Uranyl 
nitrate does not crystallize well from aqueous solution, but it was found 
that if a little nitric acid is added, it crystallizes readily in fairly large 
monoclinic prisms. This recrystallization was repeated ten times from 
acid solution, and finally twice from aqueous solution. Finally the pure 
nitrate was converted to the oxide by ignition in platinum. A second 
sample, used in the preliminary series, was prepared by repeated 
fractionation of the mother liquors of the first sample. 

Since this work was carried out, Sir William Crookes * has published 
the account of several methods by which he was able to prepare specimens 
of uranyl nitrate which were not radio-active. The radio-activity of 
uranium has hitherto been supposed to be characteristic of this element. 
Crookes has shown, however, that this is not the case, but that the 
active element can be separated by treatment with ether, by fractional 
crystallization, or by treatment with excess of ammonium carbonate. 
Unfortunately none of the pure oxide prepared for this investigation 
remained, hence it is impossible to test directly its radio-activity. Since 
two of Crookes's methods were used in purifying our material, viz. the 
ammonium carbonate treatment and fractional crystallization, it is highly 
improbable that our oxide was radio-active. In repeating Crookes's 
work with nitrate made from some of the same material used in pre- 
paring our best nitrate, it was found that a sample of the fifth crystalliza- 
tion gave no trace of action on twenty-four hours exposure to a quick 
photographic plate. The material used in this experiment had not been 
submitted to the ammonium carbonate treatment. When it is con- 
sidered that the material used for our atomic weight determinations was 
first put through the carbonate process, — in itself sufficient to remove the 
radio-active element, — and then was recrystallized twelve times as 
nitrate, it would seem that our pure oxide must have been free from 
all radio-active material. 

* Proceed. Lond. Royal Soc, 66, 409 (1900). 


There is another phase of this subject that deserves to be considered, 
namely, the possible effect of radio-active matter, even if present, upon 
the atomic weight value. The purest specimen of radium or "polonium" 
yet obtained has consisted of a mixture containing probably little more 
than fifty per cent of the active element, as nearly as could be estimated. 
This highly impure material, however, possesses 8,000 times the radio- 
activity of uranium. The radio-active power of the pure material is 
undoubtedly very much greater than that of the impure mixture. Con- 
sequently the quantity of ratio-active substance necessary to give to 
uranium the comparatively slight degree of activity that it possesses must 
be exceedingly minute. Giesel has recently shown * that a quantity of 
radium so small that it cannot be detected by sulphuric acid is sufficient 
to affect a photographic plate. Crookes also says on this point, " Con- 
sidering my most active UrX does not contain sufficient of the real 
material to show in the spectrograph, yet is powerful enough to give a 
good impression on a photographic plate in five minutes, what must be 
its dilution in compounds which require an hour, a day, or a week to 
give an action ? " f Even in the ordinary active uranium compounds it 
is most unlikely that the active element — if indeed it is an element — 
could possibly be present in quautity sufficient to exert any influence 
whatever upon the atomic weight of uranium. 

Pure carbon was obtained by ignition of sugar. Large, clear crystals 
of the best " rock candy " of commerce were ground up in a porcelain 
mortar and ignited at low heat in a platinum dish as long as organic 
gases were given off. The resulting charcoal was then powdered in an 
agate mortar and ignited in a hard glass combustion tube ; first in a 
stream of pure, dry nitrogen, and finally in a stream of bromine vapor. 
In this way the carbon was freed from any impurities which might, if 
present, be acted upon during the sublimation and contaminate the 
sublimate. Owing to the presence of undecomposed carbohydrates, or 
possibly of water, most of the bromine was converted into hydrobromic 
acid. Heating in bromine was continued until acid fumes ceased to be 
given off. Finally, the carbon was again heated in a current of dry 
nitrogen. Five grams of carbon, thus prepared, left no visible or weigh- 
able residue after combustion in oxygen. 

The method of bromine purification was essentially identical with that 
used in many other atomic weight investigations in this laboratory, and has 

* Berichte der deutschen chemischen Gesellschaft, 33, 3569 (1900). 
t Proceed. Lond. Royal Soc, 66, 422 (1900). 


been proved by long experience to be the most efficient and satisfactory. 
Commercial, "pure" bromine was partially freed from chlorine by 
shaking with a fifteen per cent solution of potassic bromide. One fourth 
of the bromine was then converted to calcic bromide by running it 
slowly into milk of lime in the presence of a large excess of ammonia. 
The calcic bromide solution was filtered and concentrated by evapora- 
tion, and the rest of the bromine was added to it. A little zinc oxide 
was then added, and after standing over night the bromine was distilled, 
nearly free from chlorine. Most of the iodine is removed as zinc 
iodate. After redistilling the bromine, in order to remove any calcium 
bromide that may have spattered over in the first distillation, it was con- 
verted into hydrobromic acid by slowly dropping it into a mixture of 
red phosphorus and hydrobromic acid. The red phosphorus was at first 
washed free from chlorides. The hydrobromic acid, containing some 
free bromiue, was distilled. The free bromine liberates any iodine 
which may have escaped the zinc oxide. The first portion of the distil- 
late, containing free bromine and iodine, and organic matter, was rejected, 
and so was the last portion, which may have contained traces of arsenic. 
The hydrobromic acid was then converted into bromine by distilling over 
pure manganese dioxide previously treated with sulphuric acid and 
washed. One half the bromine is obtained by the manganese dioxide 
alone. As soon as no more bromine comes off, a little redistilled sul- 
phuric acid is added, and the rest of the bromine was obtained. It was 
then redistilled several times, rejecting the first and last portions, and 
finally dried over pure phosphorous pentoxide. 

The silver precipitation also presents no new features, except, perhaps, 
its somewhat unusual thoroughness. Partially purified silver was dis- 
solved in nitric acid, diluted, and precipitated with pure hydrochloric 
acid. After thorough washing the chloride was reduced by invert sugar 
and sodic hydrate which had been purified by electrolysis. The metallic 
silver was thoroughly washed, dissolved in nitric acid, and again precipi- 
tated as chloride and reduced. It was then dried and fused on charcoal ; 
the lumps of silver were cleaned with sand, dissolved in pure nitric acid, 
diluted to a volume of two litres, and again precipitated with pure hydro- 
chloric acid. The resulting chloride was then digested on the steam 
bath with aqua regia, washed, and once more reduced by invert sugar 
and sodic hydrate. After drying, it was fused on pure sugar char- 
coal. The buttons of silver were cleaned with sand, and then puri- 
fied electrolytically, a small portion being dissolved in nitric acid to 
serve as the electrolyte, and the rest serving as anode material. The 


crystals of electrolytic silver were then dried over potash and fused 
in vacuo on a boat of pure lime. The buttons of silver thus obtained 
were treated with nitric acid to remove the surface, dried, and kept over 
potash. A second sample was obtained by fusing in vacuo electrolytic 
silver which had been prepared from the silver bromide obtained in Dr. 
Baxter's work upon cobalt, which was known to be very pure. 

Ilydric dioxide was purified as follows : To a solution of the ordinary 
commercial peroxide prepared for medicinal use, was added a solution of 
baric hydroxide, which had been purified by recrystallization. The pre- 
cipitated baric dioxide was washed until a nitric acid solution of the 
same showed no trace of halogen. It was then added to pure dilute sul- 
phuric acid, and the resulting solution of hydric dioxide was filtered and 
distilled in a partial vacuum. The solution thus obtained showed no trace 
of halogen, and left no visible residue on evaporation in platinum. 

Ammonium sulphide was made from pure ammonia, which had been 
redistilled in platinum, and pure sulphuretted hydrogen. It left no visible 
residue on evaporation in platinum. 

Hydrochloric and nitric acids were redistilled in a platinum still, and 
throughout the work platinum vessels were used wherever possible. 

Water was twice redistilled, once over alkaline potassic permanganate, 
and again over acid potassic sulphate from a Jena glass flask, a block-tin 
condenser and Jena glass receiver being used. 

The Results of the Analyses of Uranous Bromide. 

The method of analysis has been already fully described. 

The analyses recorded in the first series were made by adding an 
excess of silver nitrate to the solution of uranyl bromide. From the 
ratio of the observed weights of uranous bromide to argentic bromide, 
the molecular weight of uranous bromide was calculated, that of argentic 
bromide being assumed to be 187.885. From the results obtained from 
this preliminary series the weight of silver necessary to precipitate the 
bromine in one gram of uranous bromide was calculated. In the subse- 
quent determinations the exact weight of silver required was weighed 
out, as nearly as possible, and dissolved in pure nitric acid with suitable 
precautions to avoid loss. The exact end point was reached by standard 
hundredth normal solutions of argentic nitrate and hydrobromic acid, by 
means of the nephelometer.* After determining the end point a slight 
excess of argentic nitrate was always added, and the weight of the total 

* Richards, These Proceedings, 30, 385 (1894). Z. anorg. Cliem., 8, 269 (1895). 



argentic bromide determined. Thus from each of these analvses two 
distinct ratios were obtained as a basis for the calculation of the molecular 
weight of uranous bromide, — the ratio of uranous bromide to argentic 
bromide, and that of uranous bromide to silver. 

As would naturally be expected from the complexity of operations 
involved, determinations of the sodium in the filtrates from the argentic 
bromide gave unsatisfactory results. The large quantity of filtrate and 
wash waters had to be evaporated to small bulk, the uranium precipi- 
tated, and the sodium determined in the residue. It seemed advisable to 
make a series of separate analyses for sodium only, and use the average 
percentage of sodium found as a constant correction. This method was 
used in the work upon cobalt and nickel.* 

Accordingly three alkali determinations were made, wholly in platinum, 
the material not coming in contact with glass at any time except during 
the original collection and weighing of the sublimed bromide. The sub- 
limate was dissolved in pure water, in a platinum dish, and the uranium 
was precipitated with pure ammonium sulphide. The ammonium sul- 
phide was freshly prepared for each analysis, wholly in platinum. It left 
no residue on evaporation in platinum. The precipitated sulphide was 
digested on the water bath to expel most of the excess of ammonium 
sulphide, filtered through a platinum funnel, and the filtrate and wash 
water evaporated to small bulk in a platinum dish. The sodium bro- 
mide was then converted to sodium sulphate and weighed. The follow- 
ing table contains the data and result : — 


Weight of 

Weight Sodic 


Weight of 

Sodic Bromide. 

Per cent 





















The average of these three determinations, 0.095, per cent, is practically 
identical with the amount of sodic bromide found in the cobalt and nickel 
work, which was 0.10 per cent. The porcelain tubes used in this inves- 

* These Prcoeedings, 34, 339, 365 (1899). 


tigation were of the same manufacture as those used in the nickel and 
cohalt work, and since the method of preparation of the three bromides 
was practically the same, probably the quantity of sodium extracted from 
the tubes by the action of the hot bromine vapor was the same, — on the 
average, — in all three cases, and not far from 0.10 per cent. Conse- 
quently, in calculating the following results, this value was used as a 
constant correction. The effect of applying the correction is to raise the 
calculated atomic weight about two tenths of a unit. Of course by this 
method the quantity of sodic bromide calculated will vary somewhat from 
the exact quantity present, in individual determinations. The average 
result, however, will undoubtedly vary but little from the result obtained 
if the alkali could be determined in each sample. It certainly is very 
much nearer the truth than the results to be obtained by the cumber- 
some method of determining the alkali in the filtrate from each precipita- 
tion of argentic bromide. 

Analysis No. 2 was rejected on account of contamination of the 
uranous bromide by shreds of asbestos from the packing of the jacket, and 
No. 4 was not used because the combustion tube cracked during sublima- 
tion, rendering probable the formation of some oxybromide. The silver 
required in analysis No. 6 was determined for practice preparatory to 
the final series, being 0.9087 gram when all corrections were applied. It 
is not included in the table, since its nature was essentially preliminary. 
As usual, all weighings were reduced to the vacuum standard. While all 


O = 16.000 ; Ag = 107.93 ; Br = 79.955. 
First Series (preliminary). UBr 4 : 4AgBr. 

No. of 


Total Weight 
of Uranous 
Bromide + So- 
dium Bromide 
iu vacuo. 

Weight of 
for NaBr. 

Total Weight 
of Silver 
in vacuo. 

Weight of 

for NaBr. 

Parts of Ura- 
equiv. to 100 
parts Argen- 
tic Bromide. 

Weight of 






















Average 74.289 




Second Series. UBr 4 : 4AgBr. 

No. of 

Weight of 
Uranous Bro- 
mide + Sodic 
in vacuo. 

Wt. of Ura- 
nous Bromide 
for Sodic 

Total Weight 
of Silver 
in vacuo. 

Weight of 

for NaBr. 

Parts of Ura- 
nous Bromide 

equiv. to 100 
parts Argen- 
tic Bromide. 




Weight of 














Average . 


. 74.296 


Third Series. UBr 4 : 4Ag. 

No. of 

11 (8) 

Weight of 



with all 



Weight of Sil- 
ver in vacuo 
(not corrected 
for Sodic 




Weight of 


with all 





Wt. of Uranous 
Bromide corre- 
sponding to 
100 grams 




Weight of 


Average 238.52 

Average of all determinations . . 
Average of six final determinations 


the weighings were actually made to the hundreths of a milligram the 
final corrected data are rounded off to the nearest tenth of a milligram, 
since the deviations of the results show that the hundredths could have 
had no significance. 

The extreme difference between the highest and the lowest values in 
the preliminary series is 0.33 unit, in the second series 0.09 unit, and in 
the third series 0.14 unit. At first sight these variations seem large, but 
their relative magnitude appears smaller when the great molecular weight 
of uranous bromide, 558.34, is taken into consideration. Thus the 
extreme percentage error of the preliminary series is 0.06, while those 
of the last two series are only 0.016 and 0.024 per cent respectively. 


The so-called " probable error " of the average atomic weight computed 
from the six analyses numbered 7 to 12 inclusive, if each is given the 
same weight, is 0.015. That is, according to the theory of least squares, 
the atomic weisht of uranium should be between 238.515 and 238.545. 

The magnitude of the maximum deviations in these two final series is, 
moreover, about as large as would have been expected from known ana- 
lytical uncertainty. The observed variation in the amount of sodic 
bromide, for which a constant correction had to be applied, would account 
for three quarters of it, and the rest, corresponding to less than the 
tenth of a milligram in the weighings, might easily be due to unavoidable 
errors of weighing or manipulation. 

Further evidence of the trustworthiness of the figures is to be found in 
the comparison of the amounts of silver used in analyses 10, 11, and 12, 
with the corresponding amounts of argentic bromide, found in analyses 
7, 8, and 9. This comparison is given in the following table, which 
gives the weights of silver corresponding to 100.000 parts of argentic 

Weight of 

in vacuo. 

Weight of Ag 
iu vacuo. 

Quotient x 100 = 

per cent of Silver in 

Argentic Bromide. 







The result not only verifies the mechanical work, but affords evidence 
that the precipitate must have been pure argentic bromide. Clearly, 
then, the analysis is as accurate as need be. Further repetition of the 
process might reduce the so-called " probable error," but could not 
change the average by a significant amount. In the present state of the 
question, the method seems to have been carried as far as expediency 

It is worth while to inquire whether or not the method may conceal 
some source of constant error beyond the reach of the experimental 
precautions detailed above. Such an error could hardly have occurred 



during the analysis ; for every step of this procedure was verified by 
confirmatory evidence. If a flaw existed, it must have been in the 
purity of the original substance. Since the observed atomic weight is 
lower than the former results, it is important to examine into only 
those possible irregularities which could have had the effect of lowering 
the apparent value. 

The probable impurities tending to lower the atomic weight are, first, 
sodic bromide; second, hydrobromic acid; third, free bromine; fourth, 
uranic pentabromide ; and fifth, an unknown metal with a lesser equiva- 
lent. The first impurity was found to be present, its amount was deter- 
mined, and a suitable correction was applied. The second could not have 
been formed during the sublimation of the uranous bromide, because com- 
pounds of hydrogen were scrupulously excluded. If formed by the action 
of water after the sublimation, the atomic weight would have appeared 
too high — for moist uranous bromide emits hydrobromic acid instead of 
absorbing it. The third impurity, free bromine, could hardly have been 
imprisoned or absorbed by the sharply crystalline salt to any appreciable 
extent, since the concentration of the bromine vapor in the issuing gases 
was but small. 

The evidence in regard to the absence of pentabromide is fairly conclu- 
sive, although somewhat indirect. All attempts by many iuvestigators 
to form this compound have failed, in spite of the recognized existence of 
the corresponding chlorine compound. It seemed possible, however, 
that while this compound is not formed at high temperatures, lower 
temperatures might permit the addition of the extra bromine. Accord- 
ingly the preparations used in Analyses 7, 8, 10, and 11, were cooled 
in a current of dilute bromine vapor, instead of in pure nitrogen. The 
presence of a comparatively small amount of pentabromide would make 
a very decided difference in the quantity of bromine found. Hence the 
essential agreement of the average result of these analyses, 238.50, with 
the average result of all the others, 238.52, is good evidence of the 
absence of uranium pentabromide. 

With regard to the fifth possible impurity nothing can be said except 
to point out the many operations involved in the purifications. These 
seem to point toward probable purity ; but it is nevertheless to be re- 
gretted that lack of time prevented the analysis of many different fractions 
of material, prepared in varying ways. 

The presence of oxybromide would of course cause low bromine anal- 
yses, and too high an apparent atomic weight. Therefore this possible 
cause of error need not be considered, even if the oxybromide had ever 


been made in the absence of water. In the light of all these consid- 
erations, there would seem to be no good reason to question the purity 
of our bromide. 

On comparing the result of this investigation, 238.53, with that of 
Zimmermann's, 239.59 (the only previous work worthy of serious consid- 
eration), the difference of over a unit seems at first to be one of great 
magnitude. The percentage difference (0.45%) is however smaller than 
many a difference which often has been passed by unheeded in small atomic 
weights, such as those of magnesium or aluminum. This point illustrates 
the difficulty of obtaining results with high atomic weights which can 
satisfy the cursory reader. 

Nevertheless, such a difference is far too great to pass unchallenged. 
It seems highly probable that the greater part of it is due to the 
previously discussed sources of inaccuracy in Zimmermann's method, — 
especially to the difficulty of wholly re-oxidizing the lower oxide. 
The failure to oxidize half a per cent of the uranous oxide, involving an 
error in the weight of only 0.017 per cent of the total weight of the 
substance, would account for the discrepancy. 

Hence it seems not unlikely that the atomic weight of uranium is 
really as low as 238.53. Nevertheless, the question cannot be looked 
upon as conclusively settled. Certainty can be obtained only by the 
application of a new method, radically different from the two just com- 
pared. Our experience of nearly four years of varied work seems to 
indicate that the search for such method will not be an easy one. The 
many degrees of quantivalence of uranium and the unsuitable properties 
of its compounds combine to render the problem one of unusual difficulty. 
When face to face with a problem of this kind one cannot but admire 
Stas's wisdom in selecting chiefly univalent elements with powerful 
affinities in order to prove the constancy of the atomic weights. 

The result of our analyses of uranous bromide may be summed up in 
the following words: If oxygen is taken as 16.000, and bromine as 
79.955, the atomic weight of uranium appears to be not far from 

Cambridge, Mass., U. S. A. 1897-1901. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 15. — February, 1902. 




By Theodore William Richards. 

Investigations on Light and Heat made and published whollt or in part with Appropriations 

prom the rcmford fund. 




By Theodore William Richards. 

Presented January 9, 1901. Received January 14, 1901. 

I. Presentation of the Facts. 

In a paper first presented to the American Academy of Arts and 
Sciences in May, 1900, then revised and printed in the Proceedings a 
year later,* certain interesting facts concerning the significance of chang- 
ing atomic volume were pointed out and emphasized. It was shown 
that the contractions and expansions occurring in liquids and solids during 
chemical reaction are related to the affinities concerned, as nearly as we 
can estimate those affinities. A greater affinity seems to produce a 
greater contraction, if the compressibilities concerned are equal. It 
seemed possible that this idea might have very fundamental and far 
reaching applications as to matters of fact, and might lead moreover to a 
somewhat new conception of the atomic h} r pothesis. 

Many such applications have already been tested with plausible results. 
The complete detailing of the ramifications of this idea would need the 
compass of a book ; in the present paper the attempt will be made 
merely to sketch the relations of a single side of the question. 

In the paper already referred to the suggestion was made that the 
heat of chemical reaction might be traceable to the work done by chemi- 
cal affinity in compressing the substances concerned. The discussion 
below will show the close relationship which exists between these facts. 

The most serious difficulty in the way of determining the relationship 
is the extreme scarcity of data concerning compressibility. Obviously 

* These Proceedings, 37, 1 (June, 1901). 


the compressibility of a compound contains too many possible variables 
to form at once the certain basis of exact reasoning ; and among elements 
only mercury, lead, copper, and iron in the uncertain form of steel, seem 
to have been even crudely studied.* The problem is moreover compli- 
cated by the fact that the coefficient of compressibility diminishes as the 
pressure increases. 

The work which is needed in order to compress a given substance to a 
given extent can only be computed accurately when the varying com- 
pressibility through the whole range is known ; and since the pressures 
involved in the present question are clearly many thousands of atmos- 
pheres, the precise solution of the problem seems to be a distant matter, 
although by no means impossible. 

By a process of approximation some light may be obtained, however. 
If one selects a single series of compounds, such as the chlorides, it is 
obvious that a large part of the compressibility throughout the series 
should correspond to the compressibility of the chlorine. In those cases 
where the compressibility of the metal is smallest, the change of volume 
would be due almost solely to the compression of the non-metal. 

In view of these considerations, the first approximation should be 
obtained by comparing the actual contractions taking place during the 
formation of amounts of substance containing the same weight of chlorine 
with the heat evolved in each case. The starting point in each case is 
liquid chlorine, having a molecular volume of about 50 (or an atomic 
volume of about 25) at 20°. The heat of formation of the chloride is 
usually given in tables of data as starting from chlorine gas, under 
atmospheric pressure ; hence the latent heat of evaporation and expan- 
sion of tbe chlorine should be subtracted from the usual values in order 
to institute a precise comparison. f However, these quantities cannot be 
large in proportion to the heat of combination with the metal, and they 

* Landolt and Bornstein, Phys. Cliem. Tab., pp. 268, 278 (1894). Unless 
otherwise stated, all data used in this paper were taken from this admirable book 
of tables. 

t The latent heat might be approximately calculated from the data of Knietsch 
(Landolt and Bornstein, p. 80 (1894)) as follows : — 

_ RT*dP 8.32 X (293.5)2 X 0.19 . 

Q = PdT ~ 6.62 X 1 = Joules, or 20.5 

kilojoules, between 20° and 21° C, for the evaporation of one gram-molecule. The 
wide deviations from the gas-law exhibited by chlorine render the calculation 
very uncertain. It is enough, however, to show that the value is relatively small. 
The heat absorbed on expansion must also be in doubt on account of the same 



would apply equally in each case ; hence in the first approximation the 
usual values for the heats of combination may be given without affecting 
the argument. 

The table of data herewith collected compares the contraction which 
takes place when two gram-atoms of chlorine combine with some other 
substance, and the heat evolved during the operation. 

Comparison of Contraction with Heat of Formation involved in 
the Synthesis of Chlorides. 




Atomic Vol. 

Metal -f 

11 times 

Atomic Vol. 







tion corre- 
to 2 Atoms 

Heat of 
ing to 2 








[Carbon IV ] . 







Sodium . . 














Potassium . 















Iron 11 . . 







Nickel . . 



50.4 (?) 




Cobalt . . 







Copper . . 







Zinc . . . 







Strontium . 







Silver . . 







Cadmium . 



46.5 (?) 




Barium . . 







Mercury 11 . 







Thallium . 







Lead . . . 







The parallelism of the heat of reaction and the contraction which 
results from it, is obvious from the table and the accompanying diagram, 
vol. xxx vii. — 26 



100 200 300 400 500 600 700 800 900 kj. 
10 20 30 40 50 60 70 cubic centimeters. 






















which represents graphically the results recorded in the table. The ele- 
ments are arranged in the order of their atomic weights, and both sets of 
data are drawn as abscissae, because this method of treatment will facili- 
tate later comparison, and because it obviates certain irregularities due to 
periodicity. Each division stands for ten cubic centimeters of contraction 
on the left hand curve, and a hundred kilojoules of heat-energy on the 
right hand curve. 

The correspondence is obviously too close to be the result of chance. 
One is forced to believe that a fundamental relationship exists between 
the two phenomena. 

In these curves the compressibility is ascribed wholly to chlorine, and 
that of the other substance is neglected ; but when the latter is large, it 
also must enter into the problem. Unfortunately our data concerning 
compressibility are unusually limited ; but approximate calculations, 
based upon such as are known or may be guessed, show that at least 
some of the irregularities in the parallelism may be ascribed to this 

We may thus formulate the following law : The work needed for the 
compression involved in the formation of one solid or liquid by the combi- 
nation of two others is approximately proportional to the heat evolved. 

"While the general tendency of the law is manifest, and a correction 
for individual compressibilities would undoubtedly make it more so, there 
are nevertheless several exceptions to be explained. These may arise 
from several causes ; in the first place, many specific gravities of solids 
are known only approximately ; * in the next place, it is important that 
the same modifications of each substance should enter into each calcu- 
lation. A plausible explanation has been found even for the excep- 
tionally wide deviation exhibited by argentic chloride ; but this point 
will not be dwelt upon now, since it is being submitted to the test of 

The relation may be further illustrated by a table giving the data for 
a few bromides, and of course many other data might also be given. In 
order to eliminate as much as possible the contraction of the metal, it is 
well to choose for comparison a common non-metal possessing a compara- 
tively large coefficient of compressibility, hence both chlorine and 
bromine serve well. 

As a final example, the case of a single metal combining with several 

* See Richards, These Proceedings, 31, 1G3 (1895); also Ostwald, Zeitschr. 
phys. Chem. 3, 143 (1889). 



non-metals may be cited. Potassium is chosen in this last case because 
it is probably among the most compressible of metals. 

Comparison of Contraction with Heat of Formation involved in 
the Synthesis of the Bromides. 



Volume of 


Atomic Vol. 
Metal + 
n times 

Atomic Vol. 

Volume of 



tion corre- 
to 2 Atoms 

Heat of 
to 2 Atoms 















Calcium . 







Zinc . . . 














Cadmium . 














Comparison of Contraction with Heat of Formation involved in 
the Synthesis of Potassic Halides. 


Volume of 

Sum of At. 
Vols, of Metal 
and Halogen. 

of Salt. 

Difference or 

Heat of 

Chlorine . 
Bromine . 
Iodine . . 









When the more obvious experimental errors have been considered, 
two important questions at once suggest themselves : Does this propor- 
tionality signify equality, or is some of the energy of compression stored 
as potential energy and not manifested as heat? Again, if this equality 
exists, is it always exact, or is it modified by subordinate secondary 
effects ? 

* These values are calculated from very accurate determinations of specific 
gravity made recently in this Laboratory. See These Proceedings, 31, 163 

t Approximately corrected for heat of evaporation and expansion. 



These questions cannot be answered at present. The total amount of 
work done in any case cannot be computed without a knowledge of the 
compressibility of the substances involved throughout the total range of 
volume, as has already been said. Unfortunately no suitable data exist 



300 400 500 600 700 800 kilojoules. 
30 40 50 00 cubic centimeters. 

CaBr 2 
ZnBr 2 
CdBr 2 













capable of satisfying the conditions of the problem. Before long I hope 
to present such data, and to formulate answers to both questions ; for 
the present the following unsatisfactory approximation is suggested as 
being better than nothing. 

From the study of many allied data I have been able to form an ap- 
proximate evaluation of the compressibilities of sodium and chlorine. 


If one accepts these guesses, and imagines that the compressibilities 
decrease with decreasing volume according to the usual approximate law, 
one arrives at the conclusion that an amount of work equivalent to the 
heat of combination of sodium and chlorine would correspond to a 
change of volume in the system not far from the observed change 
of volume. The outcome is complicated by the fact that even in ele- 
ments, but especially in compounds, there may be superposed several 
grades of compressibility. This can be explained hypothetically as fol- 
lows : When the molecule is composed of two atoms, the highly com- 
pressed portion of each atom at the point of chemical union should have 
a much smaller coefficient of compressibility than the slightly compressed 
remainder of the molecule. If the molecule is polymerized, there will 
probably be yet other grades of compressibility in the various parts. The 
only object of a calculation so uncertain as this is to show that the heats 
of formation are of the same order of magnitude as the work involved in 
the compression. 

In spite of the inevitable difficulties in the way of interpretation — 
difficulties which seem to be inherent in the problem — the presumption 
is strong that the chief source of the heat of chemical combination is the 
work performed in compressing the material. Since the heat of reaction 
is known to represent only approximately the free energy of the reaction, 
while the compression may really represent the affinities at work, one 
would hardly expect the relation to be exact. The generalization is a 
question of fact ; it does not necessarily involve any atomic hypothesis, 
and can be regarded as uncertain only on account of the uncertainty 
of the data at present accessible. It is my intention to carry out 
the experimentation necessary to place the law on a more stable 

In the same way any other manifestation of attraction or affinity, such 
as cohesion or adhesion, should have a compressing effect and therefore 
evolve heat. The superficial and limited nature of these phenomena 
would ordinarily prevent any appreciable rise in temperature. In some 
cases, however, as in the adsorption of liquids and gases by porous ma- 
terial exposing a large surface, such a heating effect has been actually 
observed. Thus the essential difference between water of crystallization 
and adsorbed water is that the former penetrates the mass, while the 
latter is merely superficial. 

It is obvious, moreover, that the same considerations apply to solidifi- 
cation and change of allotropic form. For example, liquid phosphorus, 
yellow phosphorus, and red phosphorus have at 44° the atomic volumes 


17.66, 17.1, and about 14.1 respectively. The first small contraction is 
attended with an evolution of 0.65 kilojoules, and the second larger one 
with the evolution of 114 kilojoules of heat energy. In those cases 
where there is a transition from a more compressible union to a stabler, 
less compressible one, involving more work of compression, solidification 
would involve increase of volume, as in the case of water. 

II. A Plausible Interpretation. 

It becomes now an interesting question to determine, if possible, the 
mechanism by which this work is converted into heat. One is reminded 
at once of the compression of a gas, where the work of compression re- 
appears quantitatively as heat energy. But the compression under con- 
sideration differs from the other in detail, because in the present case the 
attraction of the two substances for one another seems to be the cause of 
their mutual compression ; and this mutual compression takes place not 
from the outside, but throughout the whole substance. 

Those who shun the atomic hypothesis and consider substance only in 
the mass, will rest contented without further attempt at interpretation ; 
but those who hold that the hypothesis is a useful tool, to be thrown aside 
when newer invention has devised a better one, will be tempted to go 

The case, considered hypothetically, seems to be this : "When two dif- 
ferent atoms possessing mutual affinity approach one another, they are 
drawn closer than they can be to their respective fellows, and in the 
process evolve heat. The " repulsion " which is often supposed to sur- 
round an atom, and prevent it from touching any other, seems to be par- 
tially overcome by the potential energy of affinity. But of what nature 
is this " repulsion" ? Ordinarily it is assumed to be due to the frequent 
impacts of a hard atom in the centre of the space; but no evidence is 
afforded of the existence of a free space. Indeed, it seems inconceivable 
that solids should retain their structure, or should be capable of retaining 
gases or liquids, if they are so loosely built up. A pile of sand would 
be stable compared to such a fabric. 

The present research points to quite a different interpretation of the 
facts. The space occupied by a solid seems to have a chemical signifi- 
cance as well as a physical one; it seems, indeed, to be as essential a 
property of the material as any other property. Since the significance of 
the total volume is a chemical one, the "free space" around each indi- 
vidual atom must also have a chemical as well as a physical significance. 


In other words, we have no right to imagine that the space is " free " or 
that there is a hard particle in the centre ; the shell is as essential an 
attribute of the atom as the centre. But how are we to account for heat 
vibration, if the atom is supposed to fill the whole space ? This question 
is important; but before answering we must consider some of the con- 
sequences of this form of compression. 

Let us imagine two highly elastic spheres ; for example, two very thin- 
walled india-rubber balls filled with gas. Imagine these to be drawn 
together by a powerful attraction resideut throughout themselves. When 
they come in contact, each will compress the other and evolve heat in 
the process. They will remain bound together and distorted, unless some 
force separates them. If the shell of an atom is elastic and compressible, 
it is only reasonable to suppose that the interior is also. In that case 
the whole substance of both of two combining atoms will suffer distortion 
from the mutual attraction of every part of their substance ; and the con- 
centration of those constituents in each atom which cause the affinity will 
thus be increased in the half nearest the other atom. The supposition that 
the affinity comes from within will cause here an essential divergence from 
the actual conditions in two balls filled with gas, in which the gas is distrib- 
uted equally throughout. As a consequence, the opposite half which is 
not combined will lose some of it attractive constituents, aud should then 
have less tendency to unite with the new substances than it had before 
its union with the first atom. This plausible influence agrees with the 
well-known facts of " false equilibrium " and the nascent state ; in fact, 
it would account in general for the permanence of slightly stable 

By the process of hypothetical reasoning given above, one concludes 
that the whole substance of the atom may be elastic. In that case heat 
vibration might consist simply in alternate condensation and rarefaction 
of the medium within the shell, started by the momentum of impact. This 
would continue indefinitely, unless the vibration were imparted to other 
substances possessing less. Such internal rarefaction and condensation 
might well tend to distend the atom if any portion of the atom were held 
by another. 

Thus, it is evident that there is no difficultv in imagining internal 
vibration in an atom which is packed on all sides closely with other 
atoms, or in explaining the mechanism of the thermal expansion of solids 
and liquids upon that basis. The chief reason for imagining a small 
hard particle with a large free space around it is therefore removed. 

Two other reasons for retaining the conception of the old atom may be 


larked ; one, the continuity of the liquid and gaseous state, and the other, 
the porosity of solids. 

In answer to the first, attention may be called to the fact that the con- 
tinuity of the liquid and gaseous condition exists actually only at the 
critical pressure ; below that point they are, as a matter of fact, discon- 
tinuous and very different. Perhaps the critical pressure is simply the 
point where the gas molecules at the critical temperature are pressed 
into actual contact. The compressibilities of very compressed gases are, 
in fact, of the same order of magnitude as those of liquids. 

Porosity is usually only manifest under very great pressure, which 
might be enough to compress the atoms into smaller space, and thus 
open orifices which previously did not exist. 

From these considerations it seems to me that the new kinetic concep- 
tion of the solid and liquid state has no disadvantages which the old 
conception does not possess, while it has many advantages which the old 
theory has not. 

But it is not the intention of the present paper to enter into the detail 
of so large a question. I hope that in the next few years I may be 
permitted to study and report upon the possible consequences of the 
significance of changing atomic volume. 

In the preceding paper and the present one, the following phenomena 
have been suggested as capable of a new and plausible interpretation if 
atoms are considered as capable of altering their volume through a wide 
range ; namely, the heat of chemical reaction, adsorption, adhesion, 
and cohesion ; ordinary solution ; electrolytic solution ; electrolytic dis- 
sociation ; the passage of electricity through solids, liquids and gases ; 
the nature of cathode rays (and probably also X rays and radium) ; the 
laws of Faraday and Dulong and Petit ; false and true equilibrium ; 
heat capacity and thermal expansion ; quantivalence ; stereo-chemistry 
and crystal form ; and the critical phenomena. 

Following papers will be devoted to a development, quantitative 
where possible, of these applications, as well as of many others. Unless 
further study reveals discrepancies, which have hitherto been concealed, 
I expect to be able to show : — 

1. That the conception is not inconsistent with the two laws of energy. 

2. That it conflicts with none of the quantitative conclusions of the 
atomic hypothesis, nor with the kinetic theory of gases, if heat be assumed 
to be due to mechanical energy operating upon atomic inertia. 

3. That it is able to interpret the actual deviations of gases from the 
gas law better than any other theory, retaining the essential import of 


the equation of van der Waals, and modifying this equation only as 
regards the changeability of a and b. 

4. That it is consistent with the varying specific heats of substances 
in the solid, liquid, and gaseous states. 

5. That with the help of this theory such physical properties as ten- 
acity, ductility, malleability, and coefficient of expansion assume for the 
first time a conceivable consistency. 

6. That upon it may be based a definition of the essential influences 
of chemical change and equilibrium. 

7. That the variable compressibility of atoms furnishes a plausible 
explanation for many of the phenomena of quantivalence, including even 
the feeble affinities holding water of crystallization and other so-called 
molecular combinations. 

8. That it explains all the tridimensional relations of material, such as 
stereochemistry and crystal form, at least as well as any other theory. 

9. That with the proviso that electrical energy is a rhythmic mani- 
festation of energy, — tending to repel itself and therefore to keep upon 
the surface of material which is susceptible to it, and hence to expand 
a free atom, — many of the electrical and magnetic phenomena of matter 
become more conceivable. 

10. That the effect of light in hastening the attainment of chemical 
equilibrium, and the possibility of storing and emitting light energy 
possessed by material, may be interpreted in a similar way. 

11. That the careful consideration of all these and other facts leads 
to a somewhat new conception of the relation between gravitation and 
chemical affinity, as well as between matter and luminiferous ether. 
This conception involves simply an antithesis of contracting and expand- 
ing tendencies, and is thus founded entirely upon an energetic basis. 

12. That the idea is capable of throwing light upon the periodic sys- 
tem, and the genesis and permanence of the elements. 

13. That it may be applied even to such astrophysical problems as 
the cause of the sun's heat. 

This is a large program ; some of it is already in manuscript, and more 
must await further exact experiment. The program is given here only to 
call attention to the wide possibilities of the consistent introduction of the 
conception of atomic compressibility into chemistry and molecular physics. 

The present paper is only one step in the direction indicated. It is 
nevertheless an important step, for it adds approximate quantitative 
evidence to the previously given qualitative evidence concerning the 
significance of changing atomic volume. 


III. Summary. 

The contents of the paper may be divided into two parts : In the first 
part is set forth an approximate generalization which rests upon facts 
alone. This part of the paper can be overthrown only by the proof that 
the facts upon which it rests are erroneous. In the second part of the 
paper a plausible hypothetical interpretation of the facts is given. This 
part of the paper stands ready to share the fate of all hypotheses, — • 
namely, to retire into oblivion if it is not capable of aiding the discovery 
of truth. 

In brief, the chief points touched upon may be summed up as follows : — ■ 

I. (a) It has been shown that the contraction exhibited during 
chemical combination is in many cases approximately proportional to the 
heat evolved. 

(b) Upon correcting the results for known differences of compressibility, 
the approximation becomes closer. 

(c) An approximate calculation of the work which would probably be 
involved by the compression of a gram-atom each of sodium and chlorine 
into the space occupied by a gram-molecule of salt showed this work to 
be of the same order of magnitude as the actual heat of formation. 

(d) From these facts and calculations the inference is drawn that the 
heat of chemical reaction is chiefly due to the energy required for the 
compression which takes place in the reaction. 

(e) Possible corrections are pointed out. 

(/) An explanation is given upon the same basis of the mechanism of 
the heat of adsorption, adhesion, and change of allotropic form. 

II. (a) While the evidence is not exact, it affords a strong presump- 
tion in favor of the hypothesis of compressible atoms. The possibly far- 
reaching effect of this simple and plausible hypothesis upon chemical 
theory is pointed out. 

(b) There is given a list of the especially prominent aspects of the 
question which will form the subjects of immediate experimental and 
theoretical study in this Laboratory. 

Cambridge, Mass., U. S. A. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 16. — April, 1902. 



By Theodore W. Richards and George W. Heimrod. 



By Theodore William Richards and George William Heimrod. 

Presented February 12, 1902. Received January 29, 1902. 


In a recent preliminary paper * it was shown that the disturbing in- 
fluences in the common silver " voltameter " (or better, coulometer f) are 
due to the concentrated liquid which falls from the anode. In order to 
avoid the inaccuracy thus caused, it was suggested that the anode be 
surrounded by a fine-grained porous cup, which is capable of preventing 
this heavy liquid from reaching the kathode. 

The weight of silver deposited by a given current in such a voltameter 
was found to correspond very closely to the amount of copper deposited 
at the same time in a copper voltameter shielded as much as possible 
from all discoverable sources of error ; hence it seemed probable that the 
new voltameter gives the true value of the electrochemical equivalent of 

In a matter so important as this, however, it seemed advisable to ob- 
tain much more information concerning the constancy and trustworthiness 
of the new instrument, as well as to discover if possible the mechanism 
of the phenomena which rendered the older form untrustworthy. The 
investigation described below was undertaken with these objects. 

I. The Constancy of the Porous Cup Voltameter. 
The first problem was to determine if two instruments in series would 
always give identical results; in other words, to find if the new voltam- 
eter is always consistent with itself. 

* Richards, Collins, and Heimrod, These Proceedings, 35, 123 (1899). 

f The word " voltameter " was devised before electrical dimensions were 
understood. It is moreover too much like the universally used and suitable word 
" voltmeter." Now that the former instrument is placed upon a firm basis of 
accuracy, it may appropriately receive also an accurate name ; and it is hoped that 
the new word "coulometer" may replace wholly the anachronism. 



Nine such duplicate experiments were made. The first of these was 
a crude trial, and need not be recorded ; the eight others are given in 
the following table. 

The apparatus employed was precisely like that described in the pre- 
vious paper. For the sake of easy reference, the description is repeated 

Small cylinders of Pukal's porous ware (Berlin), suitable for osmotic 
pressure experiments, were used to enclose the anode in order to prevent 
the heavy anode-solution from reaching the kathode. These vessels 

were 50 millimeters high and 

—J A * 20 in diameter ; their walls 

were not much over one milli- 
meter in thickness. Their 
impurities were removed by 
boiling with nitric acid and 
thorough washing with water. 
Before being used they should 
be carefully searched and 
tested for cracks or imperfec- 
tions. They were suspended 
in the solution by means of a 
platinum wire hung upon a 
glass hook, which insulated 
the wire from the electric 
connections. By means of a 
siphon, or a small pipette 
with a rubber top, the liquid 
within the cup was always 
kept at a lower level than 
that without, so as to prevent 
outward filtration. 

The kathodes consisted of 
large crucibles weighing only 
GO grams, although they were 
capable of holding 120 cubic 


Figure 1. — Porous Cup Voltameter 
(§ actual size). 

A, glass hook for supporting anode. B, glass 
ring for supporting porous cup. C, silver anode, centimeters; they were pro- 
D, porous cup. E, platinum kathode. vided with lips. A crucible 

exposes a smaller surface of 
liquid to the impurities of the atmosphere, and gave in our experiments 
a more evenly distributed deposit than a bowl. 


The anodes were bars 5xlXl centimeters of the purest silver, sup- 
ported by silver wires and not enclosed in filter paper ; and the electro- 
lyte usually contained ten grams of pure, freshly prepared argentic 
nitrate in a hundred cubic centimeters of solution. 

The manipulation was simple. The platinum crucibles were cleaned, 
dried at 160°, and weighed after three or four hours' cooling in a large 
desiccator kept in the balance-room. In order to prevent leakage during 
the electrolysis, the several stands were insulated by separate glass plates, 
and all the connections were air lines. The apparatus was protected, as 
in the earlier experiments with copper, by a miniature house with walls 
of fine cotton cloth, which helped to exclude dust. When the current 
was broken, the electrolyte was removed, the silver was rinsed twice 
with water, a third filling with water was allowed to stand in the cru- 
cible for two or three hours, and a fourth one remained in it over niffht. 
The wash-waters were collected and filtered if the silver showed any 
tendency to break off. In such cases a Gooch crucible was employed to 
collect the particles ; and a very small filter, afterwards burned, served 
to catch the minute flakes of asbestos detached from the mat. On the 
next morning the crucibles were washed once more, rinsed twice with 
pure alcohol, and finally dried and weighed as before. This method of 
treatment gave opportunity for the diffusion of mother liquor from the 
intricate recesses of the crystallized mass, while it did not run the risk of 
dissolving silver which may attend the use of boiling water for washing. 

As has been said, the crucibles were dried at 100°. It was subse- 
quently shown, in agreement with the results of Lord Rayleigh and Mrs. 
Sidgwick, that a red heat is needed to drive off all the included liquid 
from the silver crystals; but since the amount included is fairly constant, 
this fact does not interfere with the availability of the uncorrected data 
for the present purpose of comparing one weight of silver with another. 

Weighings were made upon the balance which served for the weigh- 
ings in the earlier work upon copper, — one which has served also for 
many determinations of atomic weights. Its results with small objects 
may he depended upon to within ^ milligram. All weighings were made 
by double substitutions, a similar vessel being used as a tare, and the 
weights were of course carefully standardized. Since the question con- 
cerned merely the comparison of silver with silver, the results were not 
at first corrected to the vacuum standard. 

The results show that the average difference between the weights of 
the silver deposited in two crucibles placed in series was less than the 
tenth of a milligram, or only about four parts in one hundred thousand. 
vol xxxvii. — 27 



Considering the size of the platinum vessels weighed, this average agree- 
ment is all that could be expected ; hence the test of the constancy of the 
apparatus seems to have been satisfactory. 


Test of the Constancy of the Porous Cup Voltameter. 

No. of 

Voltameter I. 

Weight of 


Voltameter II. 

Weight of 


























per cent. 



There is of course nothing in this table to show whether the figures 
represent the weight of silver which ought to have been deposited by the 
quantities of electricity employed. It may be that the error of the old 
voltameter was merely reduced, and that a small constant error still re- 
mained. The most probable cause of such a remaining error seemed to 
be the possible diffusion or migration of the heavy anode-liquid through 
the bottom of the porous cup, in spite of the fact that it was continually 
removed by means of a pipette or siphon. In order to prevent this, the 
bottom and a few millimeters of the sides of a porous cup were filled 
with melted paraffin, which effectually sealed the pores. The upper part 
of the sides only served to allow the passage of the electricity. A tenth 
comparison showed that a current which deposited 1.83370 grams of 
silver in this cup deposited 1.83375 grams in the ordinary porous cup 
coulometer. This difference is no greater than a possible experimental 
error; hence we may conclude that the effect of the diffusion is impercep- 
tible. It will be shown later that the substance which causes the chief 


irregularity of Lord Rayleigh's voltameter is probably a heavy complex 
ion ; hence it is not surprising that both the migration-rate and the 
diffusion-rate of the impurity is small. On the other hand, when the 
porous cup is too coarse-grained or too large, or when the anode solution 
is allowed to rise too high and thus filter through, the effect of the diffu- 
sion begins to be manifest. The same error begins to show itself when 
the viscosity of the solution is diminished by increasing temperature, as 
we showed in the preceding paper. 

If now the formation of ionized silver at the anode is attended by such 
disturbing side reactions, it is reasonable to assume that a remedy may 
be found in the use of an anode of some other metal. For this purpose 
zinc seemed to offer peculiar advantages ; it possesses only one degree of 
quantivalence, and has so great a solution-tension as to avoid the possi- 
bility of contaminating the deposit of silver at the kathode. 

A zinc rod (so-called " C. P.") served as the anode in the following 
two experiments, and it was surrounded by a ten per cent solution of 
zincic nitrate prepared from the same material by solution in nitric acid 
(standing for a week over zinc), filtration, and crystallization. The 
kathode solution consisted of a ten per cent solution of argentic nitrate, 
as usual. 


The Effect of a Zinc Anode. 

No. of 

Wt. of Silver 
in Ordinary 
Porous Cup 

Wt. of Silver 

in Voltameter 


Zinc Anode. 











per cent. 



A peculiar reaction was observed during this electrolysis. The zinc 
rod was covered with a copious white flaky precipitate, and a marked 
test for nitrite was observed in the supernatant solution.* Thus the 
ionization of the zinc is attended with the formation of basic salt and 

* See also Senderens, Comp. Rend., 104, 504 ; also Ber. d. d. oh. Ges., 20, 197 R 



zinc nitrite. The N0 3 ' ion must have been decomposed into NO./ and 
oxygen. This same reaction takes place when silver serves as an anode 
in its nitrate solution, although to a much smaller extent. 

In spite of the irregularities just described, the deposition on the 
kathode proceeded in a perfectly regular manner, and the figures show 
that as much silver was deposited in one cell as in the other. 

Still another means of testing the porous cup voltameter was found in 
its comparison with a device which eliminates the porous cup wholly, 
but which nevertheless keeps the anode solution quite away from the 
cathode. This device consists in placing the anode at the bottom of a 
tall beaker filled with a concentrated solution of argentic nitrate (200 
grams of the salt in a litre of solution), and arranging the kathode in 
the upper part of the vessel.* The anode solution becomes heavier 
and remains around the anode, while the kathode solution becomes 
lighter and rises to the surface. In order to prevent this dilution 
around the kathode from diminishing too much the concentration of the 
contiguous liquid, it is well to sink the kathode at least two centimeters 
below the surface. A circular disk of platinum wire gauze, f six centi- 
meters in diameter, was used as the kathode, since many holes in gauze 
permitted the ready escape upward of the impoverished electrolyte. 
The gauze was bent around a stout circular platinum wire, and the disk 
was stiffened by four radial wires, and was hung rigidly from the centre. 
The vertical distance between this kathode and the anode was about 
seven centimeters. The anode consisted of a plate of pure silver, and its 
platinum connecting wire was protected from the solution by an enclos- 
ing glass tube. 

The chief trouble encountered in manipulating the voltameter thus 
constructed is the danger of losing fine crystals of silver from the flexi- 
ble gauze. In the two experiments described below every precaution 
was taken to avoid this source of error, and it is believed that no appre- 
ciable weight was lost. Another disadvantage of the gauze is the fact 
that metals deposited upon it are very apt to include minute quantities of 
electrolyte because of the interstices arising from its woven structure. 
Even silver deposited in a crucible contains some included mother 
liquor, and that deposited on the gauze contains much more. In the 
two experiments given below, the first deposit on the gauze lost 0.42 
milligram on gentle ignition in a large porcelain crucible, and the 

* Merrill, Phys. Rev., X, 169 (1000). 

t Paweck, Zeitsch. fur Berg. u. Huttenwesen, 46, 570 (1898) ; Winkler, Ber. d. 
d. ch. Ges., 32, 2192 (1899). 



second lost 0.72 milligram, while the two crucible deposits lost respec- 
tively 0.20 and 0.24 milligram. These losses, accompanied by audible 
decrepitation, must have been due to retained electrolyte. 
In the table the weights of the iguited precipitates are given. 

Comparison of Porous Cup Voltameter with Wire Gauze Voltameter. 

No. of 

Weight of 

Silver in 

Porous Cup 


Weight of 


deposited on 



Percen tage 








per cent. 


Average € 

rror . . . 

. +0.08 


The gauze kathode thus showed an average surplus of less than a 
tenth of a milligram. But even this slight error is explicable, for it is 
clear that the argentic nitrate held by the electrolyte must have left silver 
nitrite or silver behind on heating. If we assume that the temperature 
of ignition was enough wholly to decompose the electrolyte, the average 
loss of 0.57 milligram would correspond to a residue of about 0.1 milli- 
gram, while the corresponding residue from the weaker solution used in 
the porous cup voltameter could not have exceeded 0.02 milligram. The 
difference between these two figures is exactly equal to the observed 
difference between the gauze voltameter and the porous cup voltameter, 
so that the two may be said to give precisely identical results. 

An important point connected with this experiment is the fact that 
the kathode surface available for deposition on the gauze had an area of 
less than half that on the inside of the large crucible. Hence the current 
density in the gauze voltameter must have been over twice that in the 

There has thus been accumulated a convincing array of evidence indi- 
cating that the porous cup voltameter affords a means of depositing the 
amount of silver which really corresponds to the quantity of electricity 
sent through it. The numerical averages may be summed up in a brief 
table as follows : — 


Average deviation of two porous cup voltameters in series = ± j^-j*^ 
Difference caused by sealing bottom of cup = — looooo 

Difference caused by use of zinc anode = ± lofnjoo 

Difference (corrected) between gauze voltameter and cup voltameter ± 

The agreement of these results is as close as could be expected, since 
the discrepancies do not exceed the possible experimental error. With 
Lord Rayleigh's method, when two precisely similar voltameters are 
compared, Kahle * and Rodger and Watson f have shown that an ac- 
curacy of 6 or 7 parts in 100,000 can be obtained. On the other hand, 
the least variation of size of kathode or anode, or of any other condition, 
causes large deviations which may amount to ten times as large an error. 
In our experiments given above, the most radical changes of method were 
introduced, without affecting the results. 

Among the efficient forms of apparatus described above, the porous 
cup voltameter with a silver anode is the most convenient. Hence for 
the further purposes of this paper it will be chosen as the standard 

II. The Separate Effect of each Anode Irregularity. 

It is obvious from the study of earlier work that more than one irreg- 
ularity exists at the anode in a silver cell ; and the separation and iden- 
tification of the individual effect of each irregularity became a matter of 
considerable interest. The outcome was instructive as an example of 
the multitude of hidden minor influences which so often modify the ob- 
vious outcome of chemical experiment. 

Qualitative testing revealed not only acid, but also nitrite, in the anode 
liquid ; and in those cases where the anode is very small, some experi- 
menters have indicated the formation of highly oxidized compounds of 
silver. Moreover, the singular crystalline silver dust which forms 
around the anode demands an explanation. In order to solve the prob- 
lem, of course an obvious available method was to introduce artificially 
each impurity in turn into the pure liquid around the kathode in the 
porous cup voltameter, and study its effect on the gain in weight of the 

The first impurity to be investigated was the nitrite. In order to pre- 

* Wied. Ann. N. F., 67, 22 (1899). 
t Phil. Trans., 186 A, 633 (1895). 


pare the nitrite, we had recourse at first to a method used by Proust.* 
lie has found that on boiling an argentic nitrate solution with finely di- 
vided silver, the nitrite is produced in quantity. In repeating this ex- 
periment, powdered silver reduced from purest silver chloride by the 
Stas method was boiled in a ten per ceut argentic nitrate solution. 
Nitrite was indeed formed, but a very fine film of crystallized metallic 
silver was formed on the surface ; a complication which seemed to point 
towards the existence of a reaction similar to the solution of copper in 
cupric sulphate. But it was found that pure silver nitrite in neutral 
silver nitrate solution likewise deposits a fine silver mirror on exposure 
to the light; hence the silver in both cases must be supposed to result 
simply from the decomposition of the nitrite. The solution boiled with 
silver was filtered through a Gooch crucible, and after cooling was em- 
ployed iu a voltameter with a porous cup. The solution containing the 
nitrite deposited 2.27945 grams of silver, while pure argentic nitrate in 
another standard voltameter deposited 2.27944 grams, a difference of 
only 0.01 milligram. (Exp. 15.) 

Evidently the nitrite present had no effect at the kathode ; and the 
liquid in an ordinary voltameter could hardly contain more nitrite than 
this solution which had been boiled with metallic silver. In order to 
pursue the matter further, however, we prepared silver nitrite from pure 
potassium nitrite and silver nitrate.f Pure potassic hydrate was neutral- 
ized with nitric acid ; the nitrate was re-crystallized and fused in a silver 
crucible, and the resulting mixture of nitrate and nitrite was extracted 

Standard vs. Voltameter with Solution Saturated with AgN0 2 . 

No. of 

Type of Voltameter 
containing Nitrite. 

Wei prh t of 


in Standard. 

Weight of 
Silver iu Vol- 
tameter con- 
taining AgN0 2 . 




Filter paper volt. 







per cent. 


* Journ. de Physique, March, 1806, 211 ; also Nicholson's Journal, 15 : 378. 

This reference has evidently been lost, since no text-book, including Dam- 
mer, gives it, although all mention Proust's observation. After a long search 
through the journals published in Proust's days, the reference was rediscovered. 

t Victor Meyer, Liebig's Ann., 171, 23 (1874). 


with boiling water. The great bulk of nitrate may then he removed by 
one crystallization. If to the mother liquor is added a solution of ar- 
gentic nitrate, the argentic nitrite will precipitate at once as a thick 
yellow paste. This is washed and re-crystallized from hut water, until 
the color has changed to white. The pure nitrite was dissolved in a 
nitrate solution to saturation, and this was employed, first, with a jjorous 
cup (16), and second, with a paper-wrapped anode (17). 

The results show that a saturated solution of nitrite really has the 
effect of increasing the kathode deposit. 

Since the increase due to a paper-wrapped anode over the weight 
found with a porous cup would have been from 0.04 to 0.08 per cent, the 
nitrite caused an increase of about the same amount in each case. But 
this' increase happens only when the solution is saturated with nitrite ; 
hence it is interesting chiefly as a limiting effect, and can hardly bo im- 
portant in solutions of nitrite as dilute as those formed spontaneously 
around the anode. The formation of nitrite is evidently the result of 
the breaking up of the N0 3 - ion into the nitrite ion N0 2 ~ and ox3 r gen, 
and the latter is probably taken up by the silver in forming one of the 
oxidized compounds to be discussed later. 

It is not at all surprising that this side reaction should take place to a 
small extent. The current is normally carried from the anode to the 
solution by the formation of the silver ion from the metal ; but a slight 
tardiness in this reaction (which might be named " physico-chemical in- 
ertia") would result in assistance from the anions in the neighborhood. 
They would seek to adjust the potential by discharging their negative 
electricity on the anode. Of course the most plentiful anion in the vicin- 
itv is the nitrate ion ; its deionization would make possible the form- 
ation of the nitrite ion anil oxygen, which might at once oxidize the 
silver plentifully present.* The reaction might be written thus: — 

N0 8 + 3Ag = Ag + + N0 2 - + Ag 2 0. 

Thus the electrolysis of a strong solution of argentic nitrate might be 
predicted to result, in the neutralization of a previously acid solution — 
a prediction which agrees with the fact discovered by Rodger and 
Watson f with thirty per cent solutions of argentic nitrate. It is pos- 
sible that a higher oxide also would be found if the anode were small. 

* The probable presence of silver in supersaturated solution around the anode 
will be shown later. 

1 Rodger and Watson, Phil. Trans., 186 A, 031 (1895). 


But Kahle * found that in weaker solutions acid is produced instead 
of being removed, and we have verified his results. Clearly this must be 
due to yet another irregularity. When the solution is dilute and neutral, 
oxygen and hydroxy], ions are both present in appreciable amount, ac- 
cording to modern electrochemical interpretation. Their greater ease of 
deionizatian would compensate for their relatively small concentration, 
and traces of negative electricity might be carried out of the solution 
through their agency with the formation again of argentic oxide, or even 
oxygen gas. The reaction would, however, leave an excess of ionized 
hydrogen (acid) in solution, a state of affairs not paralleled in the case of 
the nitrite. This would explain the phenomena in question. 

But would not the argentic oxide at once dissolve in the simultaneously 
formed acid, and thus form argentic nitrate again? Or, in other words, 
does argentic oxide form with silver an oxide-complex of any degree of 
stability ? Hellvvig f in a recent paper has shown that the weak silver 
ion in the presence of the strong N0 3 ~ ion tends to strengthen itself by 
taking up a molecule of some other undissociated substance, as AgCl, 
A"I, A"Br, or AgCN. He has proved also that the solution actually 
contains ions like Ag 2 I + , since on electrolysis the iodine accumulates at 
the kathode, and disappears from the anode. 

In order to find if argentic oxide could in a similar way associate itself 
with the silver ion, we boiled very pure argentic oxide with a concen- 
trated solution of argentic nitrate, and filtered the solution hot. Upon 
being diluted with cold water this solution yielded a white precipitate, 
which turned gray upon standing. The precipitate was soluble in dilute 
nitric acid, hence it could not have been an argentic halide ; besides, 
every precaution had been taken to exclude the halogens. The com- 
pound precipitated on dilution must, therefore, be silver hydroxide or a 
basic salt; and a basic complex must have existed in solution. 

It is by no means inconceivable that this complex, although finally de- 
composed by acid, should not yield at once to its action. In the meantime 
the acid, diffusing at a far more rapid rate than the heavy complex, would 
have partly left the immediate neighborhood of the anode, and hence the 
heavy solution around the latter would fail with its basic load to the 
bottom of the kathode vessel. There the complex ion (possibly Ag 3 O f ) 
would be capable of transferring electricity as well as any other ion, and 
upon deionization would deposit over three times the weight of material 

* Kalile, Wied. Ann., 67, I (1899). 

t Zeitschr. anorg. Cliem., 25, 157 (1900). 



contained in the silver ion carrying the same quantity of electricity. 
Part of this material would be in the form of oxide, and would therefore 
cause dark spots on the surface of the kathode, — spots which have 
actually been noticed by other experimenters. 

This interpretation serves to explain also the very high results ob- 
tained by Lord Rayleigh in the presence of argentic acetate. The 
possibility of forming slightly dissociated acetic acid would prevent any 
considerably accumulation of ionized hydrogen, and the oxide-complex 
would grow in concentration without hindrance. This explanation 
seems more plausible than the provisional one suggested by Lord Ray- 
leigh, — namely, that the acetate itself might be carried down with the 

In order to submit these interpretations to the test of experiment, 
electrolyses were conducted with solutions saturated with argentic oxide. 
Kahle, Patterson and Guthe, and others, have likewise carried out such 
electrolyses, showing that the deposit is as a matter of fact too great ; but 
our trial is easier to interpret, because by means of the porous cup all 
anode complications were excluded, and the result of experiment gives 
the effect of argentic oxide alone. 

Three trials were made, in which a given current of 0.25 ampere as 
usual was run first through a standard porous cup voltameter, and then 
through a cell precisely similar except that the kathode solution in the 

latter was saturated with the argentic oxide, 
tains the results : — 


The following table con- 

Standaed vs. Standard saturated with Ag 2 0. 

No. of 

Weisht of 


in Standard. 

Weight of 

Ag Standard 

with Ag 2 0. 












per cent. 




, 055 

The solution after boiling with silver oxide thus really contains, there- 
fore, some ion heavier than Ag + . Since this has been formed directly 



from the oxide, it probably contains Ag 2 0, and may be assumed to have 
the formula already given, Ag 3 + . Thus the preceding interpretation 
is confirmed. 

The next question which arises concerns the permanence of this com- 
plex in the presence of acid. In order to test this, a solution of argentic 
nitrate was saturated with argentic oxide, and then treated with a slight 
excess of nitric acid. After a short time, perhaps an hour, electrolyses 
were made with this solution in series with the standard, as usual. 

Standard vs. Standard saturated with Ag 2 0, but afterwards acidified. 

No. of 


of Ag 

in Standard. 

Weight Ag 
from Sol. with 
Ag 2 0+HN0 3 . 











per cent. 


The results are somewhat less regular than usual, but clearly most if 
not all of the oxide-complex had been removed by the acid. Thus, while 
the complex is capable of existence in a neutral solution, the speed of its 
reaction with acid results in its decomposition in a short time, as would 
be expected. 

It is possible that this oxide-complex is not the only one capable of 
being formed at the anode. Kahle, Sulc,* Mulder and Heringaf and 
others, present evidence showing that with a small anode, where both 
silver and nitrate ions would be less available for transferring electricity, 
a highly oxidized compound having some such formula as Ag 7 NO n may 
be formed. This compound is capable of dissolving in acids, forming a 
brown solution ; and it may be responsible for the colored rings which 
Kahle has noticed from old acid solutions. The fact that after boiling 
with metallic silver such solutions cease to yield colored rings is evidence 
that the foreign compound is a highly oxidized substance. 

In spite of the fact that the nitrite, the oxide-complex, and the per- 

* Sulc, Z. anorg. Cliem., 12, 89, 180 (1896) ; 24, 305 (1900). 
t Mulder and Heringa, Ber d. d. ch. Ges., 29<, 583 (189G). 



oxide-complex, may explain many of the irregularities observed during 
the electrolysis, they cannot explain them all. The chief questions re- 
maining to be answered concern the cause of the high results which are 
still to be obtained when all the preceding causes of irregularity have 
been eliminated, as well as the mechanism of the formation of the plentiful 
" anode dust." 

A number of facts point to the conclusion that some other complex 
compound exists in the electrolyzed liquid which is capable of deposit- 
ing metallic silver upon a silver surface. Among others is the well 
known fact that a pure silver kathode receives a larger deposit with a 
given current than a platinum kathode in the old Lord Rayleigh vol- 
tameter. It seemed to be worth while to test once more this relation, in 
order to confirm the results of Lord Rayleigh, Kahle, and others, and 
also to discover if a pure argentic nitrate solution in the porous cup 
voltameter would give like results. The following tables record the 
results of our experiments. In the first place we repeated Kahle's ex- 
periments, using an anode protected only by filter paper. 

Filter Paper Voltameter on Platinum and on Silver. 

No. of 

Weight of 


on Platinum. 

Weight of 

on Silver. 



Weight of 











per cent. 









... . 4-0.010 

There is an undeniable surplus when the deposit is made on silver. 
The main question now arises, — Is this effect due to the anode solution, or 
is it an irregularity which would come equally from pure argentic nitrate ? 
The answer to the question is easily determined by means of our porous 
cup ; a comparison of deposits made iu a standard voltameter on a silver 
and a platinum kathode .gave the following results: — 




Standard Method on Platinum and on Silver. 

No. of 

Weight of 


on Platinum. 

Weight of 


on Silver. 










per cent. 


The only difference is now in the opposite direction ; and this was due 
to known experimental error. In experiment 27 a small loss of silver 
particles in the wash-water from the silver cell produced the difference of 
0.009 per cent. It is highly probable that but for this accident, the deposit 
on silver would have been equal to that on platinum, as it is in No. 28. 
These results permit us to draw two conclusions. First, it is not the greater 
inclusion of silver salt in the crystals which increases the total weight 
when the kathode is silver. Otherwise 27 and 28 should have grown 
heavier in the same ratio. Secondly, it is the anode solution again 
which is responsible. 

The increase in the deposit on a silver surface indicates the existence of 
silver in the solution in a supersaturated state ; and this existence shows 
that there must be present some complex gradually dissociating, with 
metallic silver as one of its products. If this is the case, we should ex- 
pect to find that an oxidizing environment would be capable of removing 
this cause of inaccuracy, while substituting another easily removed by 
nitric acid. As a matter of fact, Schuster and Crossly * have shown 
that deposits made in vacuo are heavier than when made in air; again 
those made in an atmosphere of air are heavier than when made in oxy- 
gen. Of course it is understood that in all three cases the anode was 
only wrapped in filter paper. The solution usually contained fifteen 
per cent of silver nitrate, but sometimes as much as thirty per cent. 
They used the solution over and over again, thereby accumulating the 
irregular compounds. Under reduced pressure (about " 1 J inch"), the 
deposits exceeded those made in air by about 0.04 per cent, while the lat- 
ter exceeded those in oxygen by 0.04 per cent more. Myers, f who re- 
peated these experiments, found the difference between deposits in air 
and in vacuo to be as much as 0.10 per cent for 20-40 percent solutions. 

* Proc. Roy. Soc, 50, 350 (1802). 

t Wied Ann., 55, 291 ff. (1895). 



In an atmosphere of nitrogen an excess of .05 per cent in the deposit 
was observed. Our own experiments in the same direction verify the 
results of these experiments, and need not be recorded here. 

Putting aside for the moment the question concerning the nature of 
the irregular compound which can thus be partly oxidized out of exist- 
ence, it seemed worth while to discover if an oxidizing a<jent in the 
solution could remove this compound to such an extent as to cause the 
filter paper voltameter to yield accurate results. The only practical 
oxidizer for this purpose is hydrogen peroxide. A fairly strong solution 
was prepared from pure crystalline barium peroxide and dilute sulphuric 
acid. The excess of acid was removed with barium hydroxide, and the 
solution was filtered. In this solution the usual amount of silver nitrate 
was dissolved, and this was used in the large bowl as well as in the lipped 
crucible, both anodes being wrapped in filter paper. In the large bowl 
black crystals of argentic peroxide, or Ag 7 NO n , were soon formed 
which bridged across to the kathode. While the result in the bowl thus 
became useless, the crucible showed no such disturbance, but yielded 
nevertheless a deficit of .14 per cent on comparison with a standard. 
This must have been due to a side reaction, especially since the kathode 
was found covered with small gas bubbles, which were probably oxygen. 
It is possible that negative electricity was carried from the kathode to 
the solution by the ionizing of a trace of oxygen. Better results were 
obtained after the hydrogen peroxide had been diluted to one-tenth its 
former strength ; these are recorded below: — 


Standard vs. Filter Paper Voltameter containing H.,0 9 . 

No. of 


Filter paper 


+ II.,0 2 . 












per cent. 


Mean . 


The usual difference of from .04 to .08 per cent is thus reduced to 
.025 per cent ; therefore hydrogen peroxide seems to eliminate a part 


of the usual disturbance. But in view of the fact that even a deficit of 
0.14 per cent can be obtained, not much importance can be attached to 
these results, since it is impossible to say how much is due to the oxidiz- 
ing action, how much to the disturbing influence capable of causing an 
actual deficiency. 

These indirect methods of determining the presence of a complex yield- 
ing metallic silver being somewhat unsatisfactory, recourse was had to a 
more direct method. It seemed highly probable that the anode solution 
ought to be able to deposit silver without the help of the galvanic current. 
In order to show this, a porous cup voltameter was set up in the usual 
manner, except that the anode was closely wrapped in filter paper to 
retain the fine crystal powder which always separates from it. A current 
of 0.25 ampere was sent through the voltameter, and every ten minutes 
a portion of the clear anode solution was taken from the bottom of the 
porous cup by means of a small pipette, and quickly transferred to a 
small weighed platinum crucible. 

The crucible had been previously coated with silver in order to estab- 
lish equilibrium more quickly in case a compound existed in the solution 
which tended to deposit silver. 

After one hour's standing, the liquid was removed and the crucible was 
washed and dried, as a deposit from electrolysis would have been. The 
increase in weight of the crucible must represent the deposit from the 
anode solution. 


Gain in Weight of Silver in Contact with Anode Solution. 

No. Increase in Weight. 


33 0.35 

31 0.08 

35 0.25 

3G 0.63 

Mean . . 0.33 

The weight of the same crucible did not change perceptibly when 
allowed to remain in contact with a solution of silver nitrate of like con- 
centration, through which no current had previously been passed. The 
above increase in weight shows beyond a doubt, therefore, that the anode 
solution is capable of depositing on a silver surface either silver or 
some compound of this metal which must have been formed at the anode. 


The most striking evidence that a compound exists around the anode 
which is capable of depositing pure silver is the existence of the " anode 
dust." This consists of a fine powder, more or less closely adhering to 
the anode. Examination with the microscope indicates that this powder 
consists of minute crystals, which have every appearance of being metallic 
silver. Rodger and Watson * analyzed the air-dried powder, and found 
as a matter of fact that the metal is essentially pure. The contrary con- 
clusions of Myers f and others may have been based upon results obtained 
with small anodes, where argentic peroxide may have been formed. 

In our experience the weight of this dust is approximately propor- 
tional to the area of the silver anode, with a given current. It seems 
highly probable, then, that the silver at first tends to separate from the 
anode as a polymerized ion, perhaps Ag 3 + , according to the common 
principle that an unstable compound often forms the bridge between two 
stable conditions. $ The greater portion of this complex ion would be 
expected to break up at once into the normal argentic ion and metallic 
silver (Ag 3 + = Ag + + 2Ag), the latter forming the " anode dust." The 
last traces of the complex might, however, persist for some time, and 
give rise to all the phenomena seeming to be due to the existence of 
supersaturated silver in the solution. 

The argument has been so protracted that it is perhaps worth while 
to recapitulate the way in which this interpretation would explain the 
irregularities not to be attributed to the nitrite and oxycomplexes. 

This complex ion of polymerized silver undoubtedly unloads silver at a 
lower potential (*. e. more easily) than the simple silver ion. Hence the 
larger the kathode surface exposed, the greater part will the complexes 
take in the carrying of the current, and the larger will be the deposit of 
silver. This consequence of the theory agrees with the experience of 
all experimenters. Moreover, since the complexes are unstable, and 
continually tending to decompose, there must be always in solution a 
trace of molecular unionized silver, which, being supersaturated, will 
deposit on contact with solid silver. If the platinum bowl has been 
previously lined with silver, this extra deposition will begin almost 
immediately ; while if it has not been thus lined, an appreciable silver 
surface will have to be formed before the relieving of the supersaturation 
will begin to take place. This reasoning explains the invariable excess 
of the deposit upon a silver kathode over and above the amount deposited 

* Phil. Trans., 186 A, 632 (1895). t Wied. Ann., 55, 295 (1895). 

\ Ostwald, Z. phys. Chera., 22, 307 (1897). 


on one of platinum by the same current when only filter paper is used 
to protect the kathode. The results of Kahle and others seem to indi- 
cate that the presence of acid, which prevents the formation of the simple 
oxycomplex, is favorable to the formation of the ion Ag 3 + . This is 
not surprising, since the oxycomplex is probably formed at the expense 
of some of the silver which would otherwise remain in the polymerized 
condition. The fact that the kathode deposit in the common voltameter 
consists of comparatively few large crystals, while the porous cup voltam- 
eter yields a host of evenly distributed small crystals, is also explained 
by this interpretation. Solutions having a tendency to supersaturation 
always tend to deposit large crystals, for obvious reasons. When 
the absence of acid increases the number of available hydroxyl ions, 
the formation of the silver-complex is less considerable ; but the oxide- 
complexes then begin to affect the result. In concentrated solutions of 
the nitrate, this ion also enters into the irregularities. Thus the various 
irregularities are not necessarily coexistent ; circumstances determine 
which one shall play the most importaut part. 

There seems, then, to be concordant evidence of conflicting tendencies 
at work, some oxidizing and some reducing ; some tending to cause the 
dissolving of too much silver at the anode, and some to cause the dissolv- 
ing of too little. It seemed worth while to test the complicated conclu- 
sion by determining accurately the loss of weight of silver at the anode, 
in order to obtain a last ray of light upon the cjuestion. The disintegration 
of the anode renders the determination of the loss somewhat difficult ; 
but by carefully collecting all the silver powder left in the porous cup 
(when no filter paper is used) on a Gooch crucible, and adding this 
weight to the weight of the coherent part of the anode, fairly good 
results may be obtained. The following table records a series of such 
determinations. In each case the current strength amounted to about 
0.25 ampere. The experiments are arranged below in the order of cur- 
rent density. 

In some cases the anode loses more than the ideal amount, in other 
cases less. Such results can only be explained by the assumption of 
several causes of inaccuracy, and the four which we have discussed sjeem 
capable of explaining all the changes. But it is not worth while to 
trace out every possible variation ; enough has been said to emphasize 
the great complexity of the side reactions which interpenetrate a 
process apparently so simple, and at the same time to permit those 
readers who are especially interested to work out the combinations for 

voi.. xxxvii. — 28 



Loss at Anode compared with Gain at Kathode. 

No. of 

Weight of 

Loss of Anode, 
corrected for 
Silver Powder. 






























per cent. 


In the porous cup voltameter all the anode reactions which constitute 
the most serious causes of inaccuracy are safely eliminated by keeping 
the contaminated liquid within the porous cup. It is ohvious that this 
device, or some other accomplishing the same end, should always be used 
when accuracy is desired. 

III. The Purity of the Silver Deposit. 

An important question remains to be answered, namely, is the deposit 
thus obtained perfectly pure silver, or does it contain traces of included 
mother liquor? 

That impurities in the solution, such as copper, or any of the common 
metals occurring with silver, do not affect silver deposit to any great 
extent has been shown by Lord Rajleigh. Even if the solution actually 
turns green from the copper dissolved at the anode, not a trace of copper 
can be detected in the deposit. We used on one occasion commercial 
sihier nitrate with an anode of sterling silver wrapped in paper, and 
found that the difference between this and the standard was about .024 
per cent, or only about .02 per cent smaller than a similar deposit with 
the purest silver. Metals of greater solution tension than silver have 
therefore no important effect on the weight of silver, although they may 
change the structure of the silver deposit. Of course they had always 
been excluded in this work. 




On the other hand, the deposit, in common with most crystals, may- 
retain small quantities of solution or wash-water. Lord Rayleigh seems 
to be the only one who has taken this possible source of error into ac- 
count. He heated the crucibles to incipient redness, after they had been 
dried at 130° to 160°, and weighed. A loss of about .014 per cent 
was thus found. Richards and Collins, in looking for an explanation 
of the cause of discrepancies in the atomic weight of copper, had 
found by analysis the silver deposit to contain about 0.01 per cent of 

For our purpose the direct method of Lord Rayleigh seemed better 
than the indirect analytical one. The deposits, which had been dried 
thoroughly at 100° and weighed, were heated over an alcohol lamp to 
constant weight. Care was taken to heat the whole crucible evenly, and 
to use as high a temperature as possible without the formation of an 

Loss of Weight of Silver Deposits on heating. 

No. of 

At 150°. 

At Incipient 

—0.10 Big. 






per cent. 
































































alloy, — although several times this could not he prevented. For heat- 
ing the deposits on platinum gauze (see Tahle IX), a small oven was 
constructed from a large porcelain crucible, covered by a platinum fun- 
nel. The platinum disc was supported by a wire reaching through the 
tube of the funnel. In this case, the silver in the platinum crucibles 
with which that on the gauze was to be compared, was heated in the 
oven also, in order to expose both to the same temperature. Since the 
figures of this comparison are given in Table IX, it is necessary only to 
tabulate here the loss observed in crucibles when heated directly. Of 
course ^allowance has been made for the very slight hygroscopic loss 
(0.10 milligram) which a platinum crucible without silver deposit would 
have undergone. The silver films were usually those remaining from 
some of the preceding determinations. 

This percentage loss is slightly higher than that given by Lord Rny- 
leigh, and still larger than that determined indirectly by Richards and 
Collins. It is evident that the amount of included mother liquor varies 
according to the rate and mode of deposition, and it is quite possible that 
different average amounts were really included in the several investiga- 
tions. The inclusion is probably chiefly in recesses in the platinum 
kathode. The differences in included liquid given in the above table are 
of the same order as the differences in the uncorrected weights of silver 
given at first ; * hence we may ascribe at least a part Of the differences 
in the early table to inclusion of mother liquor. 

All this evidence unites in indicating that even under the best condi- 
tions the silver does not exceed a purity of 99.99 per cent ; and in apply- 
ing a correction, one should obviously use the value found in the particular 
investigation under review. 

IV. The Atomic Weight of Copper. 

Having thus clear light upon the various errors of the silver voltam- 
eter, it became a matter of great interest to recur to the original ques- 
tion which started the whole investigation, namely, the quantitative 
accuracy of Faraday's law. 

Accordingly, a voltameter like that used by Richards and Collins f — 
a modified form of Lord Rayleigh's instrument — was compared with 
a standard porous cup voltameter, neither precipitate being ignited. The 

* See page 418. 

t These Proceedings, 35, 133 (1899). 




eighteen results, including three given in the last paper, are recorded 
helow : — 

Comparison of Porous Cup with modified Lord Rayleigh Voltameter. 

No. of 


Weight Ag 
in Standard 
(Porous Cup). 

Weight Ag in 
Filter Paper 







per cent. 

A. 37 





A. 38 





A. 39 































































































Mean . 


The comparison of the deposits thus shows that when the anode is 
wrapped in paper, the deposit is on the average greater by 0.041 per cent. 
This average difference is smaller than that given in the previous paper, 
but it is probably more accurate, because it comprehends so many deter- 


minations. The wide deviations between the individual determinations 
illustrate the uncertainty of a voltameter in which the anode is merely- 
wrapped in filter paper. 

When to this difference is added the amount (0.018 per cent) caused 
by the included mother liquor, it is obvious that the weight of silver 
observed in the experiments upon Faraday's law made by Richards 
and Collins must have been 0.059 per cent too heavy. This would 
cause the observed electro-chemical atomic weight of copper (63.563 *) to 
be too small by the same percentage. Correcting for this error, the 
atomic weight of copper calculated from the results of the experiments 
upon Faraday's law becomes 63.601, while the most probable value 
found in purely chemical ways is 63.604. f 

The agreement is as close as the probable accuracy of the electrolytic 
determinations. Thus good experimental evidence is furnished, showing 
that Faraday's law holds rigorously true in aqueous solution at ordinary 
temperatures. Apparent deviations are simply due to the disturbing 
effect of side reactions. 

V. The Electrochemical Equivalent of Silver. 

It becomes now an important matter to determine, if possible, a cor- 
rection which might be applied to the methods of earlier physical ex- 
periments upon the electrochemical equivalent of the ampere. Such 
correction must at best be an unsatisfactory expedient ; the ouly really 
satisfactory method of proceeding would be to repeat the work wholly, 
using: the new voltameter as a chemical measure of the current. But 
such a proceeding involves an expenditure of time not now at our dis- 
posal ; hence it seems not wholly fruitless to attempt the correction of 
the older results. 

The series of comparisons of the standard with the filter paper voltam- 
eter just given (p. 422) will hardly serve for the purpose, since the 
latter voltameter changes in its indications with every change of form ; 
and the two comparisons with Lord Rayleigh's form, given in the 
previous paper, form too small a basis upon which to make so serious a 
correction. Hence another series of these experiments was made, in 
which the porous cup voltameter was compared directly with a voltameter 

* This result was obtained by extrapolation for a copper kathode of zero area. 
It harl a " probable error " of 0.004, and possibly contained a source of error tending 
to make it slightly too large. 

I Richards, These Proceedings, 26, 293 (1891). 


made exactly according to Lord Rayleigh's directions. These are given 
below, together with the two determinations given in the last paper. 


Comparison of Porous Cup with Original Rayleioh Voltameter. 

No. of 

Weight of 
Silver in 


Weight of 

Silver in 

Lord Rayleigh's 







per cent. 

A. 40 





A. 41 





















. +0.058 

This is 0.017 per cent more than the average of the preceding series. 
Probably a mean of the average of the two series, or +0.050 per cent, 
represents as nearly as possible the correction to be applied to Lord 
Rayleigh's voltameter. This value is not only an average of averages, 
involving twenty-three determinations, but is also very nearly the mean 
between the two extreme results 0.012 and 0.003. It may probably be 
relied upon to within 0.01 per cent of the total weight of the silver. 

It finds support in some results given in Kahle's* paper. He made a 
comparison between an ordinary voltameter and one in which the anode 
solution was constantly siphoned off and thus prevented, more or less 
perfectly, from reaching the kathode. The solution in botli voltameters 
was strongly acid, but equally so. The siphon voltameter deposited, in 
good agreement with the above results, 0.0.3 per cent less silver than 
the ordinary voltameter. 

The fact, however, that the extremes vary from .012 per cent to .093 
per cent indicates that unless great care is taken in the way in which 
the anode is wrapped, in the strength of the current and in the size of 
the anode, the depositions in the ordinary voltameter according to Lord 
Rayleigh are untrustworthy. 

* Wied. Ann.N. F., 67, 30 (1899). 



In order to correct Patterson and Guthe's results, it became necessary 
to repeat comparisons of the standard with the voltameter containing 
old solution saturated with oxide, as used by them. 

Standard vs. Patterson and Guthe's Method. 

No. of 



Weight of 
Silver in 

Weight of 
Silver in 
P. <&G. 






per cent. 

A. 43 






A. 44 







3- 6-01 

















2 02217 




4- 1-01 



2.31734 • 




4- 4-01 







5- 8-01 







. 0112 

This result is perplexing, and much lower than the average computed 
from the first two determinations, which was given in the preceding paper. 
It indicates that the Patterson and Guthe method gives results 0.0G per 
cent higher than those given by Lord Ravleigh's method, while Patterson 
and Guthe's own comparisons give a difference of 0.1 1 per cent.* Evi- 
dently the saturated-oxide method is more variable in different hands 
even than Lord Rayleigh's. Perhaps the safest number to use in the 
correction is the average of both, 0.085 per cent above the Lord Ray- 
leigh method, or 0.135 per cent above the porous cup method. 

We are now in a position to make an approximate correction for the 
effect of the contaminating anode liquid in each of the more important 
investigations which bear upon the electro-chemical equivalent of silver. 
Of these, those of Lord Rayleigh, Fr. and W. Kohlrausch, K. Kahle, 

* Pliys. Peview, 7, 280. Kahle (Wieel. Ann. 67, 32, also Brit. Ass't. A. Sc. 
1892, 148), found 0.05 per cent, but his solutions were probably fresher. 


and Patterson and Guthe have attracted most attention. Since the first 
three investigations used a voltameter of the original Lord Rayleigh 
type, a correction of — 0.05 per cent should be applied to each. More- 
over, Kohlrausch and Kahle did not heat their deposits to redness ; 
hence an additional reduction of about 0.016 per cent* is necessary. 
Finally, Kohlrausch deposited the silver on a silver kathode, while 
Lord Rayleigh and Kahle made their determinations with platinum 
kathodes — a correction which leads to a further reduction of .01 per 
cent for Kohlrausch's value, or 0.076 in all. Patterson and Guthe, on 
the other hand, deposited the silver on platinum, but used old solutions 
saturated with silver oxide. Such solutions may have yielded about 
0.135 more silver than the standard. When the correction for heating 
is added to this the total reduction becomes 0.15 per cent. Thus we are 
led to the following table : — 


The Corrected Electrochemical Equivalent of Silver. 

(1) Lord Rayleigh and Mrs. Sidgwick,f 0.0011179 —0.050% 0.0011173 

(2) Fr. & W. Kohlrausch,* 0.0011183—0.076 0.0011175 

(3) Kahle,§ 0.0011183 —0.066 0.0011176 

(4) Patterson & Guthe, || 0.0011192-0.150 0.0011175 

Average ..... 0.0011175 

The greatest deviation from this average is 0.02 per cent, a remark- 
able agreement considering the variety of physical method used by the 
experimenters. Lord Rayleigh and Kahle used an electro-dynamometer 
and Kohlrausch an accurate tangent galvanometer for the calculation of 
the current, while Patterson and Guthe made themselves entirely free 
from the acceleration of gravity or the strength of the magnetic field by 
means of an absolute electro-dynamometer. Hence for the present the 
great bulk of evidence seems to favor the value 0.0011175, the mean of 
four entirely independent determinations, as the true electrochemical 
equivalent of silver. Our data also give the electrochemical equivalent 
of copper in the cupric condition as 0.00032929 gram per ampere per 

The number of coulombs attached to one gram equivalent of any 
electrolyte is therefore 96,580. 

* The average of Lord Rayleigh's results and ours. 

t Phil. Trans., 175, 411 (1884). } Wied. Ann. N. F., 27, p. 1 (1886). 

§ Wied. Ann. N. F., 67, 1 (1899). || Fhys. Review, 7, 257 (1898). 


A few more points may be touched upon here, which follow directly 
from the new value of the equivalent. A great number of physical 
instruments have been standardized on the basis of a somewhat higher 
electrochemical equivalent of silver, 0.001118. "Will they be affected 
by the lowering of this number ? Evidently not, since if the value cor- 
responding to a given mode of deposition is applied throughout, when- 
ever this method is used, no constant error can result. Thus our low 
value cannot be employed when the anode is unprotected, and the de- 
posit not heated to redness. 

Therefore, as was shown in our last paper, the discovery of a constant 
error in the silver voltameter cannot help the discrepancy which exists 
between the electrical and mechanical methods of determining Joule's 

It is to be hoped that in the future, however, all experimenters will 
use some method, such as ours, in which the anode complications are ex- 
cluded. Obviously even the present condition of electrical science de- 
mands a more precise electrochemical definition of the ampere than that 
now prescribed. 

The present research seems to define the practical unit of current 
strength no less accurately than the practical unit of electro-motive force 
has been defined. Thus in a laboratory provided with pure chemicals, 
each of these units may be established without outside help, and with 
their assistance a standard ohm may be produced without comparison 
with any other standard ohm. 

VI. Summary. 

The results of the prolonged investigation may be summed up as 
follows : — 

1. The electrochemical equivalent of silver as determined by the 
Lord Rayleigh voltameter is too high by at least 0.05 per cent. 

2. The true rate of deionization of silver can be determined by the 
use of a porous cup which prevents the solution at the anode from reach- 
ing the kathode. Results of great consistency and accuracy are then 

3. The porous cup does not introduce any new source of error, for 
without it the same low results may be obtained when the anode is placed 
below the kathode. 

4. At higher temperature the complications grow larger. 

5. The main disturbing factor is a complex silver ion formed at the 
anode and carried over to the kathode, where it decomposes, thereby 


increasing the deposit of silver. Most of this potymerized material 
decomposes at once, however, forming the silver dust at the anode. 

6. The hydroxy! ion discharges at the anode, forming silver oxide 
and probably so-called peroxide. Ionized hydrogen is thus developed. 

7. Dissolved gases affect the deposit whenever they react with the 
complex ions. ' 

8. Nitrite is formed at the anode, but has probably not much effect 
on the weight of the deposit. 

9. The deposited silver always contains included solution, varying in 
amount from 0.01 per cent to 0.04 per cent according to circumstances. 

10. A new name, coulometer, is proposed, to replace the old and 
unsuitable designation voltameter. 

11. The true electrochemical equivalent of silver is probably 
0.0011175 milligram per coulomb. 

12. Therefore, 96580 coulombs are associated with one gram equiv- 
alent of any electrolyte. 

13. The electrochemical equivalent of cupric copper is 0.00032929; 
therefore the electrochemical atomic weight of copper (G3.G01) is in 
close agreement with the chemical value (G3.604). 

14. Faraday's law is thus verified for two kathions more exactly than 
ever before. 

Cambridge, Mass., U.S.A. 

Proceedings of the American Academy of Arts and Sciences. 
Vol. XXXVII. No. 17. — March, 1902. 


New Series. — No. XXII. 

By M. L. Fernald. 

I. The Northeastern Carices of the Section Hyparrhenae. 
II. The Variation of some Boreal Carices. 

With Five Plates. 

Copyright, 1902, 

By the President and Fellows 
of Harvard College. 


New Series. — No. XXII. 

By M. L. Fernald. 

Presented May 8, 1901. Received January 31, 1902. 



The Carices of Koch's subgenus Vigneae, with its sections Acroar- 
rhenae and Hi/parrhenae of Fries, have always perplexed the systematist, 
and by the general student they have as a rule been ignored or vaguely 
referred to such characteristic species as Carex straminea or C. 
echinata. Recently, however, the generally widening interest in sys- 
tematic botany has brought together in Carex, as in other groups, a 
large mass of material ; and an attempt to identify these specimens has 
made it necessary to study in great detail the minuter but tolerably con- 
stant characteristics of the fruiting plants. 

In general, the classification of Carices has always been based upon 
characters in the inflorescence ; and although the detailed study of the 
perigynia (or utriculi) has been the final resort of the specialist, an 
attempt has been made in our manuals to separate species as much as 
possible upon the more obvious characters of the inflorescence. Thus 
Carex scoparia is described in the two current manuals as having the 
spikelets (spikes) " all contiguous or bunched " or " usually aggre- 
gated ; " while in oidy one of these works is Boott's var. minor 
given recognition, and there as a mere dwarf variety. Yet in plants 
which are undoubtedly C. scoparia the spikelets are often scattered, 
forming a loose moniliform spike ; and the northern plant described by 
Boott as var. minor has a distinct range and unique habitat, while its 
minute thick-bodied perigynia distinguish it at a glance from the more 
southern species with which it has been associated. 

The case of Carex scoparia is only one of many in which the attempt 
to rely upon superficial characteristics has led us to confuse plants 


which are genetically very distinct. Consequently, as stated, an attempt 
has been made to get at a more satisfactory basis for classification by 
studying the characteristics of the perigynia, which, naturally, are sub- 
ject to less variation than is the superficial aspect of the inflorescence 
as a whole. But since variations in texture and nerving, which are per- 
fectly evident upon comparison of specimens, are extremely difficult to 
render clear iu descriptions, it has been found advisable to employ as 
the primary basis of division, at least in the groups here discussed, the 
actual or proportional measurements of the perigynia or the achenes. 
Even this method of careful measurement may sometimes prove mislead- 
ing, but in most species the perigynia vary within certain clearly defined 
limits, and it is only the very exceptional individual which will not fit 
the system here proposed. And, although in rare cases a species thus 
presents perplexing forms in which the perigynia are not characteristic, 
many attempts to classify the members of this group have convinced 
the writer that by actual measurement alone can we safely identify 
plants of such strong outward resemblance as Carex straminea, C 
scoparia and C. tenera, or C. alata and C. albolutescens. 

As a result of these studies it has been found desirable to treat many 
plants in a manner somewhat different from that in any current synopses 
of the genus, and in some cases a study of the original descriptions and 
specimens has brought the writer to conclusions very different from 
those generally accepted by American caricologists. Some of these 
points are of slight significance, others of fundamental importance ; and, 
since it is inadvisable to complicate the synoptic treatment of the species 
with detailed discussions as to the identity and synonymy of different 
forms, the more important questions may be here discussed. 

Carex scoparia, Schkuhr, presents little difficulty, as the original 
figure is unmistakable. The species has, however, been made to harbor 
plants of very different aspect ; and a study of the fruiting characters 
shows these to fall into three groups with marked and constant char- 
acteristics. C. scoparia, itself, has the perigynium very thin and scale- 
like, with the wings so strongly developed as to minimize the apparent 
thickness of the body. This plant in its different forms is of broad 
range south and west of the Gulf of St. Lawrence. 

The other two species which have been included with Carex scoparia 
have the narrower subulate or elongate-lanceolate perigynia so little 
winged as quite to lack the scale-like character seen in that species. 
The best known of these two plants is the form described by Francis 
Boott as C. scoparia, var. minor. The material from which Boott's 


plate was drawn was collected by Tuckerman at the base of the White 
Mountains; and since it is necessary to distinguish the plant by a new 
specific name {minor having been used too often as a varietal name to 
be eligible) and since there is already a Carex Tuckermani, it is a 
pleasure to commemorate the explorations and generous services of the 
Crawford family, familiar to a long generation of visitors to the White 
Mountains. This plant with which their name now becomes associated 
is common in northern New England and about the Great Lakes, thence 
extending far northward. 

The other plant with narrow thick perigynia is more puzzling. In 
the dark brown color of its broad scales it is unlike the other forms 
which have been referred to Carex scoparia. In fact, by different 
students it has been referred with doubt to C. tribuloides, C. lepornia, 
and C. foenea as well. Yet in its perigvnium it resembles only Boott's 
C. scoparia, var. minor. This tall dark-spiked plant, which is common 
in the region of Orono, Maine, has been collected by Professor Lamson- 
Scribner and by the writer, but it seems to be unknown from other 
regions. This fact immediately suggests that it may be an introduced 
form, but a careful search through Old World material and descriptions 
fails to show anything to which it cau be referred. It is, therefore, 
here treated as a local species, taking the name of the town from which 
all our material has been collected. 

One other form of the scoparia group should be specially mentioned 
since, by an unfortuuate misinterpretation, it has already caused needless 
confusion. This is Carex scoparia, var. moniliformis, Tuckerman. A 
specimen in the Gray Herbarium from Tuckerman himself, is without 
question a slender-spiked form of C. scoparia. The variety was so 
treated by Francis Boott, in whose table 3G8 it is well represented. 
Yet in his Preliminary Synopsis of the genus Professor Bailey treated it 
without question as identical with his own C. tribuloides, var. reducla ; 
and Professor Britton, following las lead, has since made the new com- 
bination, (7. tribuloides, var. moniliformis (Tuckerman) Britton, for a 
plant very different from that to which the varietal name was originally 

Carex tribidoides, Wahl., has been clearly treated by Professor Bailey. 1 
C. Bebbii, Olney, however, which by him is reduced to a variety of that 
species, seems to be as well marked as other members of the subgenus, 
and it is here given equal rank with them. In its shorter, broader, and 

i Mem. Torr. CI., I. 54. 
vol. xxxvu. — 29 


thicker perigynia it is more nearly related to C. straminea and its 
allies. So, likewise, C. cristata, Schwein., is reinstated as a species, 
since its tolerably constant habit and its shorter, firmer perigynia place 
it as near C. straminea as to C. tribuloides. 

The diverse plants which have been treated by various authors, now 
as distinct species, now as forms of Carex straminea, fall into groups 
which are, in the main, fairly free from complexity. The attempt to 
separate these forms by color-characters has naturally led to much con- 
fusion, for plants which in bright sunlight have a strongly marked 
ferrugineous tendency, in shade are often quite green. The shape, size, 
nerving, and texture of the perigynia, however, show that almost with- 
out exception the species proposed by Willdenow, Schkuhr, Torrey, 
Schweinitz, Dewey, and other early students of the group were based on 
permanent characters. To treat all these well marked and constant 
forms as varieties of one species is adding confusion rather than clearness 
to our interpretation of the genus, especially when several of them are 
as closely related to other well recognized species. 

The identity of Willdenow's Carex straminea was settled by Professor 
Bailey 1 in 1889, and a recent examination of Willdenow's material by 
Dr. J. M. Greenman has verified Professor Bailey's conclusions. C. 
albolutescens, Schweinitz, is now well understood, as are likewise C. 
mirabilis, Dewey, C. tenera, Dewey, C. Bichiellii, Brittou (C. straminea, 
var. Crawei, Boott), and C. alata, Torrey. But C.festucacea, Schkuhr, 
C. straminea, var. brevior, Dewey, and C. foenea, var. /3, Boott, seem 
to have been less clearly understood. 

Schkuhr's Carex festucacea, according to the original description, was 
a plant with about eight spikelets subapproximate or in a loosely 
cyliudric spike, and the species is so represented in Schkuhr's figure. It 
is likewise well represented by Dr. Boott, who apparently had a clear 
conception of the species, in his table 386. Schkuhr's C. straminea, 
which we now know to be different from Willdenow's plant of that name, 
was an extreme form of C. festucacea with fewer spikelets, and until 
recently it passed as the type of the species ; i. e., C. straminea (typica) 
of Boott and others. This plant, however, was called by Dewey C. 
straminea, var. brevior, and under that name it has been treated by 
Professor Bailey. He includes with it, though, the C. festucacea of 
Schkuhr, a plant which, though closely related, is of rather marked 
appearance and of more limited range. More recently Dr. Britton, in 

i Mem. Torr. CI.. I. 21. 


restoring to specific rank G festucacea, has included in it Dewey's G. 
straw inea, var. brevior, and in the Illustrated Flora he figures the 
latter plant under the former name. But the late Dr. Eliot C. Howe, 
in his admirahle treatment of the New York Species of Carex, has 
recognized both plants, thus following the general treatment of Francis 
Boott and other earlier writers and at the same time clearing the names 
festucacea and brevior from the confusion which has recently surrounded 

Carex foenea, var. /? of Boott has had a peculiarly unsettled history. 
When Francis Boott described and figured the plant as a variety of C. 
foenea, the latter name applied to G albolutescens, Schweinitz, not to 
the true G. foenea of Willdenow. It was Boott's opinion, then, that 
the slender brown-spiked plant of the interior was a phase of what we 
now know without much doubt to be G. albolutescens. In the fifth 
edition of the Manual Dr. Gray took up G. foenea, var. ft as G. foenea, 
var. ( ?) ferruginea ; and later the plant was distributed by Oluey as a 
variety of Dewey's G tenera (G. straminea, var. aperta, Boott). In his 
Preliminary Synopsis in 1886, Professor Bailey reduced it to synonymy 
under G. straminea, Schkuhr (not Willd.), aud later in his Critical 
Studies of Types he treated this plant along with C. festucacea, Schkuhr, 
and C. straminea, var. Grawei, Boott (C Bicknellii, Britton) as iden- 
tical with C. straminea, var. brevior, Dewey (C. straminea, Schkuhr, 
not Willd.). Subsequently, however, he has taken out of his C. stra- 
minea, var. brevior, two plants, which he treats as parallel varieties, 
var. Crawei, Boott, and var. ferruginea (C. foenea, var. /?, Boott); and at 
the same time he has discussed as a species C. albolutescens, Schweinitz 
(C. foenea of authors, not Willd.). This course has greatly cleared 
the group from its former confusion ; but it is unfortunate that while 
separating C. albolutescens specifically Professor Bailey should have 
attached C. foenea, var. fi to the slender usually flexuous-spiked C. 
straminea, whose identity he had already so carefully worked out. C. 
foenea, var. fi in its stiff habit, its strongly appressed broad-ovate peri- 
gynia, and the texture of its leaf-sheaths, is quite unlike that species, 
but is very close to C. albolutescens with which it had been placed by 
Francis Boott. In these characters, likewise, it is equally close to C. 
alata, Torr., while its perigynia and the occasional awn-tips of the scales 
are so like those of the latter species as to place it nearer to that than 
to the former plant. 

The two species, Carex foenea, Willd., and C. adusta, Boott, have 
already been discussed and very clearly settled by Professor Bai- 


ley. 1 But his own C. foenea, var. perplexa has proved very puzzlino- to 
students of the groujj. In the original description of this varietv at 
least two distinct species are referred to, while the words " head erect or 
nearly so " have proved misleading for u plant with more rlexuous spikes 
(heads) than ordinarily occur in the type of the species. 

Dr. J. M. Greenman has kindly compared with Willdenow's orio-inal 
material various plants passing in America as Carex foenea, and he has 
furnished the writer with detailed camera-drawings from Willdenow's 
material. From these comparisons there seems no doubt that the origi- 
nal C. foenea was, as Professor Bailey has already stated, the smallest 
form of the species, with 4 to 9 spikelets in a suberect linear-cylindric 
spike. This is the plant subsequently described by Tuckerman as 
C. argyrantha and figured by Boott in his table 382, fig. 2. 

Professor Bailey's Carex foenea, var. perplexa was based on Boott's 
table 380 and, a portion of table 382 (presumably fig. 1), upon Olney's 
C. albolutescens (Exsicc. fasc. 1, no. 8), as well as his C. albolutescens, 
var. sparsiflora (fasc. V. no. 11). Now, the perigynia of good Carex 
foenea are strongly and conspicuously nerved on both faces, and the 
spikelets are pale green or silvery brown. The first part of var. per- 
plexa (Boott's table 380) shows a perigynium quite nerveless or only 
faintly short-nerved on the inner face ; the second component (table 
382, fig. 1) is the characteristic large form of C. foenea with crowded 
spikes of large spikelets; the third (C. albolutescens of Oluey) is, as 
represented by two sheets in the Gray Herbarium, a form betweeu the 
large state and the small typical C. foenea ; while the fourth component 
(C. albolutescens, var. sparsiflora, Oluey — at least the New Brunswick 
plant) in habit as well as in the nerveless inner face of the perigynium 
closely matches the first cited plate (Boott's table 380). From the fact, 
that vox. perplexa was proposed as a variety of C. foenea it is probable 
that its author had in mind the coarse form represented by Boott's table 
382, fig. 1, and in the present treatment of the group it has seemed 
advisable to retain that name for the large plant. 

Olney's Carex albolutescens, var. sparsiflora is represented in the 
Oluey Herbarium by two different plants. One of these, from Oregon, 
is the dark-spiked form of C. praticola which has been described as C. 
pratensis, var. furva, Bailey. The other, from Kent Co., New Bruns- 
wick, the northeastern plant which is identified with Boott's table 380, is 
much more closely related to C. adusta, Boott, than to C. foenea, Willd. 

i Mem. Torr. CI., I. 24 


From the former species it differs constantly in its more slender habit 
and flexuous elongated spikes of clavate-based spikelets, as well as iu 
smaller achenes. It is a plant of broad range from Labrador to British 
Columbia, creeping south to the coast of New England and the mountains 
of New England and New York. Since its varietal name, sparsijiora, 
is preoccupied in the genus, another specific name is here proposed in 
reference to the characteristic color of the mature inflorescence. 

The other large group of the Jlyparrhenae which has been treated 
by recent authors as the subsection Elongatae contains plants of two 
markedly different tendencies. One group is characterized by strongly 
divergent thin-edged perigynia which are spongy at base. The other 
group has ascending plump or plano-convex perigynia which are rarely 
thin-edged and are without conspicuously spongy bases. Mr. Theodor 
Holm, who has recently studied some of the members of the first group, 
includes with them Carex gynocrates and C. exilis, which by most other 
authors have been placed in the Dioicae. The texture and aspect of 
the perigynia seem to justify the treatment proposed by Mr. Holm and 
formerly for C. exilis by Francis Boott; 1 and for the group thus con- 
stituted Mr. Holm suggests the name Astrostachyae. 2 The other group, 
with ascending blunt-edged perigynia, may well retain the subsectional 
name Elongatae, since the characteristic species, C. elongata, C brunne- 
scens (C. Gebhardii), C canescens (C curtd), etc., were originally 
included in it by Kunth. 

Mr. Holm, in the paper cited, takes exception 3 to Professor Bailey's 
recent treatment 4 of Carex echinata, C. sterilis, and C. scirpoides, on 
the ground that that author had been more controlled by the original 
specimens of Willdenow and of Schkuhr than by the original diagnoses. 
That Willdenow's original descriptions do not accord well with Pro- 
fessor Bailey's conclusions there can be no doubt ; and when we are 
told by Professor Bailey that C. sterilis and 0. scirpoides are identical, 
and when he says "the figures of both G. sterilis (fig. 146) and C. scir- 
poides (fig. 180) in Schkuhr's ' Riedgraser ' are unequivocal," 5 we find 
it indeed difficult to understand his observations. An examination of 
Schkuhr's figures shows his C. sterilis (fig. 146) to be a coarse plant 
with sharp-pointed ovate scales and broad-ovate cordate perigynia with 
distinct beak shorter than the body. Schkuhr's O. scirpoides (fig. 180), 
on the other hand, is represented with broad-obloug or elliptical blunt 

1 Boott, 111., I. 17. - Holm, Theo., Am. Jour. Sci., Ser. 4, XI. 205-223. 

3 Holm, 1. c, 212. 4 Bailey, Bull. Torr. CI., XX. 422. 

5 Bailey, 1. c, 424. 


scales and deltoid-ovate obscurely short-beaked perigynia. These figures 
of Schkuhr's agree very well with his descriptions. Furthermore, they 
agree equally well with Willdenow's diagnoses, for these latter were 
essentially the same as Schkuhr's. Professor Bailey further states that 
C. sterilis and C. sc/'rpoides are identical with the common American 
plant which he had formerly treated as C. echinata, var. microstachi/s, 
a plant with lanceolate or narrowly ovate slender-beaked perigynia ; 
and for this aggregate he takes up the name C. sterilis. After thus 
bunching three very different species as C. sterilis, lie separates from 
"our so-called Carex echinata" two plants, C. atlantica and C. interior, 
with ' ; ample specific characters." 

Through the kindness of Dr. J. M. Greenman the writer has been 
able to examine camera-drawings of Willdenow's original material ; 
while from Professor Carl Mez he has received fragments from the 
original material of Schkuhr. The drawings of the Willdenow mate- 
rial of both Carex sterilis and C. scirpoides, and the Schkuhr specimens 
of C. scirpoides agree with the original diagnoses. Dr. Greenman has, 
further, compared critically specimens sent him of the different Ameri- 
can forms with Willdenow's plants and with authentic specimens of 
C. stellulata, Gooden. (C. echinata, Murray). The identification thus 
made of these forms, leads to a conclusion very different from that 
published by Professor Bailey. These results may best be stated by 
discussing separately the three clearly cut species which have been so 
unfortunately confused. 

Carex echinata, Murray (C stellulata, Gooden.). This species was 
long considered a boreal plant of broad range, and it was so treated 
by Torrey, Tuckerman, Dewey, Carey, and other early students of 
American Carices. Francis Boott distinctly implied that the European 
species occurs in British America, saying: "I have not seen specimens 
which I can satisfactorily refer to the European C. stellulata, south of 
the British provinces of North America." 1 Yet Professor Bailey has 
interpreted this to mean that " Francis Boott questioned if the Ameri- 
can plant is the same as the European C. stellulata (or C. echinata) ; " 
and in "eliminating the European species from our flora," he says: 
" Definite specific characters of separation are obscure, and yet I am 
convinced that they exist. The American plant is habitually taller 
than the European, the scales are sharper and usually longer, the 
perigynia are more strongly nerved and more attenuated or conical, 

i Boott, 111., I. 56. 


and above all, it is far more variable. . . . There are probably no 
species common to both countries, except those which are hyperboreal 
and occur through the Arctic regions of both hemispheres, being found 
in Greenland." * 

Then Professor Bailey defines his conception of the "habitually 
taller" American plant with "sharper" scales, etc., etc., including in it 
forms varying from the low slender Carex stellulata, var. angustata, 
Carey, with " narrowly-lanceolate perigynia tapering into a long . . . 
beak,"' 2 to the tall (often nearly 1 m. high) coarse C. sterilis, Willd., 
with broad-ovate perigynia, and the slender C. scirpoides, Schkuhr, with 
thick scarcely beaked often nerveless deltoid-ovate perigynia and elliptic 
blunt scales. The two latter constituents of this aggregate apparently 
do not occur outside North America and if they are included with the 
other American representative of C. echinata as one species, it is of 
course easily said that the American plant is taller or shorter, coarser or 
more slender than the European ; and certainly a species so constituted 
is " far more variable." 

When, however, we eliminate from the complex Carex sterilis of Pro- 
fessor Bailey's treatment the true C. sterilis and C. scirpoides, there is left 
a plant characterized by slender culms and leaves, the perigynia barely 
half as broad as long, and tapering to a slender conspicuous beak which 
is often nearly as long as the body. This is the C. echinata or C. stellu- 
lata of American authors and it includes as formal variations the very 
slender var. angustata, Carey (C. echinata, var. tnicrostachys, Boeckeler), 
and the tall C. sterilis, var. excelsior, Bailey, while a very coarse varia- 
tion with rather better defined characteristics is C. echinata, var. cep/ia- 
lantha, Bailey. 

This American species with the narrow perigynia has been compared 
many times by the writer with European C. echinata in a vain attempt 
to find some point of distinction. Specimens collected by Godet at 
Lignieres on the River Cher in central France are inseparable from 
Mertens' material from Sitka, and, again, Japanese specimens collected 
by Chas. Wright and by Maries are identical in their slender perigynia 
with Newfoundland plants. In order, however, to test still further the 
specific value of the American plant a portion of Allen's Labrador mate- 
rial was forwarded to Dr. Greenman at Berlin, and he was asked to 
compare it, along with other American forms, with Willdenow's types 

1 Bailey, Bull. Torr. CI., XX. 423. 
- Carey in Gray, Man. 544. 


and with other authentic European specimens of the group. In reply 
Dr. Greenman writes of this specimen : 

" No. 4. Differs from the original C. sterilis, Willd., in the following 
characters : (a) narrower, more gradually acuminate and longer beaked 
perigyuium ; {b) more oblong achene, which is less narrowed at the 
base. To me, however, your No. 4 is a perfect match for Carex stellu- 
lata in herb. Willdenow, and for European C. echinata, Murr. I am 
quite unable to make any distinction between them. The perigynial 
characters are exactly the same." 

Extreme difficulty is experienced, then, in attempting to distinguish 
the American Carex echinata from Old World material. The range of 
the American plant, too, from Labrador to Alaska, and southward in the 
mountains, immediately places the species in the hyperboreal flora from 
which Professor Bailey, at least by inference, would exclude it. In view 
of these two facts there seems, then, as Mr. Holm has already indicated, 
good reason to consider both the American and the European plant C. 
echinata, Murr. 

Carex sterilis, Willd. This plant has already been sufficiently defined 
in the discussion of Willdenow's original description and of Schkuhr's 
figure. The writer has, however, examined with much care camera- 
drawings of Willdenow's material made by Dr. Greenman and fragments 
of Schkuhr's material generously sent by Professor Carl Mez. The 
Willdenow plant, which alone is of final importance, proves to be iden- 
tical with the large species of the Atlantic seaboard recently described 
as C. atlantica. The fragment sent by Professor Mez from the Schkuhr 
herbarium is, however, from cultivated material, and is only a form of 
C. echinata with narrow perigynia quite unlike those shown in Schkuhr's 
figure and in the Willdenow plant as further shown by Dr. Greenman's 
report of his critical comparisons in the Willdenow herbarium. 

Besides No. 4, the Labrador Carex echinata, two other forms were 
sent to Dr. Greenman for comparison with C. sterilis. No. 1 is C. 
echinata, var. cephalantha, Bailey, collected by Dr. C. B. Graves at 
Waterford, Connecticut, May 27, 1896. No. 2 is characteristic C. at- 
lantica, Bailey, collected by Dr. G. G. Kennedy at Ponkapog, Canton, 
Massachusetts, July 12, 1899. Of these two plants Dr. Greenman 
writes : 

"No. 1. This differs from C. sterilis, Willd., in the following charac- 
ters: (a) longer inflorescence, more remote and slightly longer spikelets; 
(b) longer and more prominently beaked perigynium ; (c) achene less 
narrowed at the base. 


"No. 2. I am quite unable to distinguish this plant from the original 
of C. sterilis, Willd. It has the same broad-ovate, short-acuminate or 
short-beaked perigynium, and tbe same achenial cliaracters, that is, the 
achene is rather conspicuously narrowed below. The characters of the 
inflorescence are the same, except as to color. The Willdenow plant is 
more brownish : this, however, may be due, at least to a certain extent, 
to age." 

From Willdenow's original description, from Schkuhr's description 
and figure, and from Dr. Greenman's examination and drawings of the 
Willdenow plant, there seems no question, then, that Carex atlantica, 
Bailey, is the true C. sterilis, Willd. 

Carex scirpoides, Schkuhr. The characters of this species, likewise, 
are sufficiently stated in the discussion of Schkuhr's and Willdenow's 
characterizations. Material from the Schkuhr herbarium received through 
Professor Mez is identical with camera-drawings made by Dr. Green- 
man from Willdenow's plant. These accurately agree, also, with 
Schkuhr's fig. 180. This species, was, furthermore, correctly inter- 
preted by Sartwell, Carey, and Boott, and it is well represented as 0. 
stellalata, var. scirpoides in Boott's Illustrations, t. 146.** Sartwell's 
No. 36 and Boott's plate are the only exact citations given by Professor 
Bailey for his C. interior, and his description of the so-called new species 
accords well with those of Willdenow and of Schkuhr. In distinguishing 
C. interior from C. scirpoides, Bailey says that the former has " greenish- 
tawny spikes," while the latter is "fulvous;" and he furthermore de- 
scribes Schkuhr's C. scirpoides, " as the plate plainly shows," with 
"long-beaked broad-winged perigynia." How such a statement and 
such conclusions could have been made is very puzzling. There can 
be no question, however, that the figure of Schkuhr's C. scirpoides as 
interpreted by Dewey, Schweinitz, Torrey, Sartwell, Carey, Francis 
Boott, Holm, and other students of the genus, is the same as Boott's 
table 146** upon which, ii part, C. interior was founded. 

The name Carex scirpoides, Schkuhr, so long attached to this plant, 
was published in 1805, but it cannot, unfortunately, be retained for the 
species, since in 1808 Michaux published C. scirpoidea, the well known 
dioecious plant of extreme boreal and alpine regions. The next clearly 
defined name for the plant seems to be C. interior, although, as originally 
intended by its author, that name was supposed to apply to a species 
very distinct from C. scirpoides. Tuckerman, it is true, published in his 
Enumeratio Methodica the name C. stelhdata, var. scirpina, citing C. 
scirpoides, Schkuhr, as a synonym. On a preceding page, however, 


in an unfortunate endeavor to latinize one of Michaux's names, he had 
substituted C. scirpina for C. scirpoidea, Michx., not C. scirpoides, 
Schkuhr. This unfortunate citation of W C. scirpina" as a pure synonym 
of Michaux's C. scirpoidea attaches to that name a decided element of 
indefiniteuess. It is, therefore, wiser to take for the plant of Schkuhr 
and of Willdenow the more clearly defined name, C. interior. 

One other plant of the Astrostachyae has been the source of much con- 
fusion in the treatment of New England species of this group. Unlike 
Carex echinata, C. sterilis, and C. interior, the perigynia of this plant 
are broadest at the middle, thence tapering to a narrow base. In aspect 
the plant is strikingly like the largest form of C. canescens, but its thin- 
edged strongly recurved perigynia place it clearly in the Astrostachyae. 
The species is not uncommon from eastern Massachusetts to Delaware 
and central New York, and in New England herbaria it has recently 
passed variously as C. atlantica, C. interior, C. canescens, var. vulgaris, 
C sterilis, var. excelsior, &c. From notes left by the late William 
Boott it is apparent that he recognized in some of Chas. Wright's 
Connecticut material an undescribed form, but evidently he never 
described the plant. A portion of the original material of the late 
Dr. Eliot C. Howe's Carex seorsa, generously furnished the writer by 
Professor C. H. Peck, agrees in every regard with the perplexing New 
England plant, and under that name the species should now be known. 

The members of the Elongatae, as here interpreted, offer less difficulties 
than the other species of the Hyparrhenae, and special discussion is 
needed only of the forms which have been at various times associated 
with Carex canescens. These plants present two marked forms in their 
perigynia : in one plant, C. arcta, the perigynium is broadest at the 
rounded or subcordate base; while in C. canescens and C. brunnescens 
( C. vitilis, Fries) the perigynium is nearly elliptic in outline, being 
broadest near the middle. 

Carex arcta of Francis Boott was originally published by him as C. 
canesceyis, var. polystachya, but in his latest treatment of the plant he 
considered it a distinct species. As stated, its perigynial character is 
very constant. Furthermore, its rather limited strictly American range 
and unique habit quickly separate it from most forms of C. canescens. C. 
canescens, var. oregana, Bailey, said to differ from var. polystachya in 
having the " bead larger and more dense . . . becoming brownish," 
has identical perigynia with that plant, and the spikes (heads) are green 
or brownish, as are those of the eastern plant, a character dependent on 
age and exposure to light. 


Car ex canescens, L., is characterized by its glaucous color and strongly 
appressed-ascending elliptic pointed perigynia tapering very gradually 
to, the short beak. Another plant, C. brunnescens, Poir. (C. canescens, 
var. alpicola, Wahl., C. canescens, var. vulgaris, Bailey), is usually 
bright green, and the few loosely spreading-ascending perigynia are 
rather abruptly contracted to a definite serrulate-based beak. This plant 
is common in dry soils throughout the boreal sections of America and 
Europe ; while the glaucous G. canescens is a species of very wet 
situations. Under various names, G vitilis, Fries, C. Gebhardii, Hoppe, 
etc., C. brunnescens has been treated as a species, and as often agaiu as a 
variety of C. canescens. An examination of much material shows its 
characters to be essentially constant, and, though the plant superficially 
resembles small forms of C. canescens, its claim to specific rank rests 
upon a number of definite characters. 

When Carex arcta aud O. brunnescens are removed from C. canescens, 
there remains a species characterized by its glaucous foliage and ap- 
pressed scarcely beaked perigynia. This species presents in America 
three noteworthy variations. The true C. canescens, L., of northern 
Europe has the spikes 2.5 to 5 cm. long, of 4 to 7 oblong-cylindric to 
narrowly obovoid spikelets 0.6 to 1 cm. long. This plant occurs in 
Arctic America coming south to northern New England and New York, 
the Rocky Mts., and Vancouver. Rare in the eastern United States 
and Canada, the typical form of G canescens has been misinterpreted 
by recent American students, although the species was very clearly 
discussed by Francis Boott. The American plant which has passed 
as true G. canescens is, however, strikingly different in aspect, and 
consequently the typical plant has more than once been published as 
a local American variety — var. dubia, Bailey, and var. robustina, 

Another form of Carex canescens common to northern Europe and 
America is var. subloliacea. Laestadius. In this plant the spike is 
usually rather shorter than in typical C. canescens, the less approximate 
globose or short-oblong few-flowered spikelets are only 4 to 7 mm. long, 
and the smaller perigynium is nearly or quite smooth. In its smooth 
perigynium this plant approaches C heleonastes, which, however, has 
larger spikelets and perigynia and quite lacks the distinctive glaucous 
aspect of C. canescens. The var. subloliacea, which is commoner in 
northern New Eugland than is the true C. canescens, also simulates 
G. brunnescens ; but it is very canescent and the perigynia otherwise as 
in true G. canescens are essentially smooth, while in the greener C. 


brunnescens they are distinctly beaked, of more membranous texture, and 
usually with serrate margins. 

The commonest form of Corex canescens in North America is the 
plant mentioned without name by Francis Boott and figured by him 
in his Illustrations, IV. table 496. This unique American form, which in 
essential characters is like true C. canescens, differs in its elongated in- 
florescence, 5 to 15 dm. long, at least the lower spikelets very remote. 
The plant seems to have been generally treated by American authors as 
typical C. canescens, and no published name is available for it. 

The following synopsis presents the characters and ranges of the 
northeastern Hyparrhenae as now understood by the writer. In its 
preparation he has studied the material in the Gray Herbarium and the 
herbarium of the New England Botanical Club ; as well as the hundreds 
of sheets in the herbarium of the Geological Survey Department of 
Canada, kindly placed at his disposal by Mr. James M. Macoun ; those of 
the Olney Herbarium of Brown University, made accessible to him by Mr. 
J. Franklin Collins; and a series from the Fairbanks Museum at St. Johns- 
bury, Vermont, rich in forms of the scoparia group, specially accumulated 
by the director, Dr. T. E. Ilazen, for detailed study, and then generously 
forwarded to the writer. He has also been greatly assisted by the use 
of material from the private herbaria of the Honorable J. R. Churchill ; 
President Ezra Brainerd ; Doctors C. B. Graves, J. V. Ilaberer, G. G. 
Kennedy, and C. W. Swan ; and Messrs. Luman Andrews, C. H. Bissell, 
Walter Deane, E. L. Rand, W. P. Rich, and E. F. Williams. The 
identification of dubious species of Willdenow and of Schkuhr has been 
facilitated by the cooperation of Dr. J. M. Greenman while at the Royal 
Botanical Museum in Berlin, and by Prof. Carl Mez of the University 
of Halle ; and authentic material of the late Dr. E. C. Howe's Car ex 
seorsa has been generously furnished by Prof. C. H. Peck. 

HYPARRHENAE, Fries. Staminate flowers scattered or at the 
base of the uniform spikelets (only in exceptional individuals and in the 
often dioecious C. gynocrates and C. exilis the entire spikelet staminate). 

Key to Species. 1 

* Perigynia with thin or winged margins. 
•4- Perigynia ascending, the tips only sometimes wide-spreading or recurved, 
not spongy at base, the margins winged at least toward the beak. 

1 The perigynial characters are here based on study of mature plants. In gen- 
eral the perigynia at the tip of the spikelet are less characteristic than those nearer 
the middle ; and, if possible, the latter alone should be used in critical comparisons. 


- Bracts wanting or setaceous, if broad at most twice as long as the spike. 
= Plant strongly stoloniferous ; culms rising from an elongated root- 
stock : perigynium firm, 5 to (3 mm. long (4) C. siccata. 

= Plant not strongly stoloniferous ; culms solitary or in stools. 
a. Perigynia less than 2 mm. broad. 

1. Perigynia 5 mm. or more long. 

O Perigynia 7 to 10 mm. long: spikelets oblong-cylindric, pointed, 

1.5 to 2.5 cm. long (1) C. muskingumensis. 

O O Perigynia shorter (or, when exceptionally 7 mm. long, in 
shorter spikelets). 
+ Perigynia half as broad as long, plump, nerveless or obscurely 

short-nerved on the inner face (21) C.aenea. 

+ + Perigynia one-third as broad as long. 

X Perigynia thin and scale-like, scarcely distended over the 
achenes, distinctly nerved on the inner face, and promi- 
nently exceeding the subtending scales. 
§ Leaves at most 3 mm. wide : spikelets 8 to 9, glossy 
brown or straw-colored, pointed. 
Spike oblong-ovoid or subcylindric, with ascending 

approximate spikelets (2) C. scoparia. 

Spike moniliform . . (2) C. scoparia, var. moniliformis. 

Spike short-globose or broad-ovoid, the spikelets 
crowded and divergent . 

(2) C. scoparia, var. condensa. 
§ § Leaves more than 3 mm. wide: spikelets 8 to 14, green 

or dull brown, blunt (3) C. tribuloides. 

(For vars. see below.) 
X X Perigynia firm, obviously distended over the achenes, 
nervele s or obscurely nerved on the inner faces, 
equalled by the subtending scales .... (7) C. praticola. 

2. Perigynia less than 5 mm. long. 

O Perigynia thin and scale-like, scarcely distended over the 
achenes : leaves 3 to 8 mm. broad. 
-f Perigynia with appressed tips. 

Spike oblong, the spikelets approximate . (3) C. tribuloides. 
Spike moniliform, the 6pikelets scattered 

(3) C. tribuloides, var. turbata. 
+ + Perigynia with spreading tips : spike flexuous 

(3) C. tribuloides, var. reducta. 
O O Perigynia firm, obviously distended over the achenes. 

-f- Perigynia elongate-lanceolate or subulate, less than one-third 
as broad as long, at most 1.4 mm. broad. 
X Tips of perigynia conspicuously exceeding the lance- 
subulate dull scales. 

Culms 1 to 4 dm. high : leaves 1 to 2.5 mm. wide : 
spikelets 3 to 7 mm. long (5) C. Craw/ordii. 


Culms taller: leaves broader: spikelets 8 to 11 mm. long 

(5) C. Crawfordii, var. vigens. 
X X Tips of perigynia equalled by the ovate bluntish glossy 

dark scales (6) C. oronensis. 

+ + Perigynia broader, nearly or quite half as broad as long. 

X Tips of perigynia distinctly exceeding the subtending 
§ Leaves 2.5 mm. or more wide. 

□ Spikelets compactly flowered, the mature perigynia 

with recurved or spreading tips concealing the 

scales (8) C. cristata. 

n □ Spikelets with ascending or slightly spreading peri- 
gynia ; scales apparent. 
A Mature perigynia greenish or pale straw-colored, in 
loose spikelets : spikes more than 2.2 cm. long 
(if shorter, with dark chestnut scales). 
Spikelets approximate in ovoid or oblong spikes. 
Scales pale, not strongly contrasting with the 

perigynia (10) C. mirabilis. 

Scales dark chestnut, strongly contrasting with 
the perigynia . . (10) C. mirabilis, var. tincta. 
Spikelets scattered in a moniliform spike 

(10) C. mirabilis, var. perlonga. 
A A Mature perigynia brown, in dense spikelets : spikes 
at most 2.2 cm. long : scales pale brown 

(17) C. Bebbii. 
§ § Leaves narrower. 

Spike stiff, with crowded closely flowered spikelets 

(17) C. Bebbii. 
Spike flexuous and moniliform, or at least with the 
loosely flowered spikelets scattered . (11) C. straminea. 
X X Tips of perigynia equalled by the subtending scales. 

§ Spike stiff and erect, or at least with the spikelets ap- 
Spike brown or ferrugineous .... (19) C. leporina. 

Spike brownish white (20) C. xerantica. 

§ § Spike flexuous, or at least with the lower spikelets 

□ Perigynia nerveless or minutely short-nerved on the 

inner face. 

Mature perigynia straw-colored or pale brown, one- 
third as broad as long (7) C. praticola. 

Mature perigynia olive-green or bronze, one-half as 

broad as long (21) C. aenea. 

□ □ Perigynia with strong ribs the length of the inner face : 

spike silvery green (18) C.foenea. 

b. Perigynia 2 mm. or more broad. 
1. Tips of the perigynia distinctly exceeding the subtending scales. 


O Perigynia thin and scale-like, barely distended over the achenes, 
one-fourth to one-third as broad as long. 

Perigynia 7 to 10 mm. long (1) C. muskingumensis. 

Perigynia shorter (2) C. scoparia. 

(For vars. see above.) 
O O Perigynia firmer, obviously distended over the achenes, nearly 
or quite half as broad as long. 
+ Perigynia lance-ovate, about half as broad as long. 
X Leaves 2.5 mm. broad, or broader .... (10) C. mirabilis. 

(For vars. see above.) 
X X Leaves narrower. 

§ Perigynia distinctly about 10-nerved on the inner faces, 
4 to G mm. long. 
Spikelets 8 to 12 mm. long : perigynia 4.8 to 6 mm. 

long (12) C. tenera. 

Spikelets 5 to 8 mm. long : perigynia 4 to 5 mm. long 

(12) C. tenera, var. invisa. 
§ § Perigynia 3- to 5-nerved on the inner faces, mostly less 
than 4 mm. long. 
Perigynia with ascending inconspicuous tips 

(11) C. straminea. 
Perigynia with divergent conspicuous tips 

(11) C. straminea, var. echinodes. 
+ + Perigynia with broad-ovate to orbicular bodies. 

X Spike moniliform and flexuous, with mostly clavate-based 
Spikelets brownish-white ; of close-appressed obscurely 

beaked firm perigynia (14) C. silicea. 

Spikelets ferrugineous ; the abrupt slender beaks of the 
perigynia with conspicuous loosely ascending or spread- 
ing tips (12) C. tenera, var. Richii. 

X X Spike stiff (or, if flexuous, with brown or ferrugineous 
§ Perigynia 5.6 to 7.7 mm. long, very thin, scale-like, al- 
most transparent : scales blunt . . . (13) C. Bicknellii. 
§ § Perigynia less than 5.6 mm. long, firm and opaque 
(when exceptionally longer in C. alata, with aristate 
□ Scales long-acuminate or aristate : perigynia 4 to 5.5 
mm. long : achenes oblong. 
A Spike green, or finally dull brown: scales lance- 
subulate : perigynia obovate, 2.8 to 3.7 mm. broad, 
abruptly narrowed at base .... (15) C. alata. 
A A Spike dark brown or ferrugineous : perigynia 2.3 to 
2.8 mm. broad. 

Spikelets closely approximate: scales ovate-lance- 
olate : perigynia ovate, tapering gradually to 
the beak . . . . (15) C. alata, var. ferruginea. 


Spikelets scattered in a flexuous spike : scales 
lanceolate : perigynia orbicular, abruptly slen- 
der-beaked (12) C. tenera, var. Richii. 

□ □ Scales blunt or at most acutish. 

Spikelets gray-green or finally dull brown, with 
strongly appressed-ascending very firm perigynia 
3.5 to 4 (very rarely 4.5) mm. long 

(9) C. alboluteseens. 
Spikelets straw-colored or ferrugineous, with spread- 
ing-ascending perigynia 4 to 5.5 mm. long. 
Spike of 5 to 10 mostly distinct spikelets 

(16) C.festucacea. 
Spike of 3 to 6 approximate spikelets 

(16) C.festucacea, var. brevior. 
2. Tips of perigynia equalled by the subtending scales. 

O Spike stiff and erect, or at least with approximate spikelets. 
+ Spike whitish or gray-green. 
X Perigynia lance-ovate, 4 to 4.8 mm. long, nerveless on the 

inner faces, golden-yellow at base . . (20) C. xerantica. 
X X Perigynia broad-ovate to suborbicular. 

Perigynia strongly ribbed the length of the inner faces, 

2 mm. broad (18) C.foenea. 

Perigynia nerveless or faintly nerved on the inner faces, 

broader (9) C. alboluteseens. 

+ + Spike bronze or ferrugineous. 

Perigynia distinctly concave on the usually nerved inner 

faces: achene 1 mm. broad (19) C. leporina. 

Perigynia flat or convex on the usually nerveless inner 
faces, very plump: achene 2 mm. broad . (22) C. adusta. 
O O Spike flexuous, at least the lowest spikelets remote. 

+ Perigynia nerveless or only faintly short-nerved on the inner 
Perigynia ovate-lanceolate, one-third as broad as long : 

achene 1 mm. broad (7) C.praticola. 

Perigynia ovate, half as broad as long : achene 1.5 mm. 

broad (21) C. aenea. 

+ + Perigynia distinctly nerved on the inner faces. 

X Perigynia 2.8 to 4.4 mm. long, at most 2.4 mm. broad, 7- to 
13-ribbed on the inner faces, abruptly beaked. 
Spike of 4 to 9 spikelets 6 to 10 mm. long : perigynia 2.8 

to 4 mm. long (18) C.foenea. 

Spike of 6 to 15 spikelets 10 to 17 mm. long: perigynia 
3.5 to 4.4 mm. long . . . (18) C.foenea, var. perplexa. 
X X Perigynia 4 to 5.3 mm. long, 2.5 to 3 mm. broad, 3- to 5- 
nerved on the inner faces, obscurely broad-beaked 

(14) C. silicea. 
** ++ Bracts leaf-like and much prolonged, the lowest 1 to 2 dm. long : 

spikelets crowded : perigynia subulate .... (23) C. sychnocephala. 


+- h- Perigynia horizontally spreading or reflexed when mature, spongy at 
base, with thin but scarcely winged margins. 
•w Spikelets solitary and terminal, pistillate or staminate, or with the 
flowers variously scattered. 
Stoloniferous ; the filiform culms at most 3 dm. high, from filiform 

rootstocks . . . . (24) C. gynocrates. 

Not stoloniferous ; the wiry culms 2 to 7 dm. high, in caespitose stools 

(25) C. exilis. 
++ -w Spikelets 2 to several. 

= Perigynia broadest at base : beak rough or serrulate. 

a. Perigynia at most half as broad as long, finally yellowish, with 

slender beak nearly equalling the body : scales pointed. 

1. Perigynia ovate, 3 or 4 mm. long. 
O Spikelets at most 12-flovvered. 

Spike 1 to 3 cm. long, the 2 to 6 spikelets subapproximate 

(26) C. echinata. 
Spike 2 to 6 cm. long, the 2 to 4 spikelets very remote, the 
terminal with a clavate base 0.5 to 1 cm. long 

(26) C. echinata, var. ormantha. 
O O Spikelets with more flowers. 

Leaves 1 to 2.5 mm. broad : spikelets scattered, 12- to 20- 
f owered : perigynia less than half as broad as long 

(26) C. echinata, var. excelsior. 
Leaves 2 to 4 mm. broad : spikelets mostly approximate, 15- 
to 40-flowered ; perigynia half as broad as long 

(26) C. echinata, var. cephalantha. 

2. Perigynia lanceolate or ovate-lanceolate, 2.5 to 3 mm. long : spike 

of 2 to 6 approximate spikelets (26) C. echinata, var. angustata. 

b. Perigynia more than half as broad as long, firm, brownish or dark 

green, the beak one-fourth to one-half as long as the body. 

1. Scales sharp-pointed : leaves 2.5 to 4.5 mm. broad : spike 1.5 to 3.5 

cm. long ; spikelets 15- to 50-flowered : coarse plant (27) C. stcrilis. 

2. Scales blunt : leaves narrower : spike 1 to 2 cm. long ; spikelets 

5- to 15-flowered : slender plants. 

Leaves 1 to 2 mm. broad : perigynia faintly nerved or nerve- 
less on the inner faces (28) C. interior. 

Leaves narrower : perigynia strongly nerved 

(28) C. interior, var. capillacea. 
= = Perigynia broadest near the middle, less than 2 mm. broad, very 
thin and conspicuously nerved, with short smooth beak : spikelets 

remote (29) C. seorsa. 

* * Perigynia not thin-winged, ascending from the first, plano-convex. 
t- Perigynia 4 mm. or more long, long-heaked. 

Spikelets lanceolate, in a loosely linear-cylindric spike : perigynia 1 to 
1.3 mm. broad, strongly nerved : scales oblong : leaves 1 to 2.5 mm. 

broad (33) C. bromoides. 

Spikelets ovate, in flexuous spikes, the lowest very remote : perigynia 
1.6 to 1.9 mm. broad, faintly nerved or nerveless : scales ovate : leaves 

2 to 5 mm. broad (34) C. Deweyana. 

vol. xxxvii. — 30 


+- *r Perigynia less than 4 mm. long. 
++ Perigynia 2 mm. or more long. 

= Perigynia with serrulate beaks or margins. 

a. Spike elongate, from linear-cylindric to oblong. 

1. Perigynia ovate, broadest at base : spikelets mostly or all ap- 

proximate in an oblong-cylindrie spike . . . (30) C. arcta. 

2. Perigynia broadest near the middle. 

O Plant glaucous : leaves 2 to 4 mm. broad : spikelets with many 
appressed-ascending glaucous obscurely beaked perigynia. 
Spikelets 6 to 10 mm. long, approximate, or the lowest 
rarely 1.5 cm. apart : perigynia 2.3 to 3 mm. long 

(31) C. canescens. 
Spikelets 4 to 7 mm. long, subapproximate or remote : peri- 
gynia about 2 mm. long (31) C. canescens, var. subloliacea. 
Spikelets 6 to 12 mm. long, remote, the lowest 2 to 4 cm. 

apart (31) C. canescens, var. disjuncta. 

O O Plant green, not glaucous : leaves 1 to 2.5 mm. broad : spike- 
lets with few loosely spreading dark green or brown dis- 
tinctly beaked perigynia (32) C. hrunnescens. 

b. Spike subglobose, of 2 to 4 closely approximate subglobose 

loosely flowered silvery spikelets : perigynia oblong, beakless, 

nerved, 3 to 3.4 mm. long (35) C. tenuiflora. 

= = Perigynia smooth throughout. 

a. Spike whitish, silvery-green or pale brown, not ferrugineous nor 

dark brown. 

1. Spike elongate, at least the lower spikelets scattered. 

Uppermost spikelet divaricate-pedunculate, the lowermost 
subtended by a long leaf-like bract : perigynia more than 

J! mm. long (36) C. trisperma. 

Spikelets continuous in a linear-cylindric loose spike, bract- 
less or only short-bracted : perigynia 2 to 3 mm. long 

(31) C. canescens. 
(For vars. see above.) 

2. Spike subglobose, of 2 to 4 closely approximate subglobose 

loosely flowered spikelets : perigynia beakless, 3 mm. or more 
long .... (35) C. tenuiflora. 

b. Spike ferrugineous or dark brown. 

1. Terminal spikelet with conspicuous clavate base : perigynia ab- 
ruptly beaked : culms smooth (or harsh only at tips). 
O Spikelets distinct ; the lowest 4 or 5 mm. thick ; the terminal 
1 to 1.8 cm. long: perigynia pale, about equalled by the 

yellowish-brown blunt scales (38) C. norvegica. 

O O Spikelets approximate ; the lowest less than 4 mm. thick. 

Plant weak and lax : leaves involute, 0.5 to 1.5 mm. broad : 
perigynia pale, equalled by the ferrugineous acutish scales 

(39) C. (jlareosa. 
Plant stiff and upright : leaves flat, 1 to 3 mm. broad : peri- 
gynia brown or reddish, exceeding the fuscous obtuse 
scales (40) C. lagopina. 


2. Terminal spikelet without conspicuous clavate base : perigynia 
obscurely beaked, brown-tinged, exceeding the blunt scales : 
culms sharply angled, harsh and stiff : leaves flat, erect 

(41) C. heleonastes. 
Perigynia at most 1.5 mm. long, oblong-cylindric, plump, nerveless, 
beakless or with a very short broad truncate beak :. culms wiry : 
spike linear-cylindric, dull brown (37) C. elachijcarpa. 


Ovales, Kunth. Perigynia ascending or slightly spreading (when 
horizontally spreading, always with winged margins), with thin or winged 
margins, mostly with concave inner faces when mature. 

§ Ovales proper. Bracts, when present, setaceous, or, if broader, 
only once to twice longer than the spike. 

* Mature perigynia one-fourth to one-third (.24 to .36) as broad as long. 

-<- Perigynia extremely thin and scale-like, barely distended over the achenes. 

++ Perigynia 7 to 10 (average 8.3) mm. long. 

1. C. muskingumensis, Schweinitz. — Figs. 1, 2. — Culms 1 m. or 
less tall, very leafy : the loose flat leaves subcordate at their junction 
with the loose green sheaths ; those of the sterile shoots crowded and 
almost distichous : spike oblong, of 5 to 12 appressed-ascending oblong- 
cylindric pointed spikelets 1.5 to 2.5 cm. long. — Ann. Lye. N. Y. i. 66; 
Dewey, Am. Jour. Sci. x. 281 ; Bailey in Gray, Man. ed. 6, 620; Britton 
in Britton & Brown, 111. Fl. i. 355, fig. 861. C. arida, Schweiii. and 
Torr. Ann. Lye. N. Y. i. 312, t. xxiv. fig. 2; Carey in Gray, Man. 
545; Boott, 111. i. 20, t. 54; Boeckeler, Linnaea, xxxix. 112; Bailey, 
Proc. Am. Acad. xxii. 147 ; Macoun, Cat. Can. PL ii. 129. C. scoparia, 
Torr. Ann. Lye. N. Y. iii. 394, in part, not Schkuhr. C. scoparia, var. 
muskingumensis, Tuck. Enum. Meth. 8, 17. — Meadows, swamps, and 
wet woods, Ohio to Manitoba and Missouri. July, August. 

*+ ++ Perigynia at most 6.5 (very rarely 7) mm. long. 
= Perigynia 5 to 6.5 (average 5.7) mm. long. 

2. C. scoparia, Schkuhr. — Figs. 3, 4. — Culms 0.2 to 1 m. high, 
mostly slender and erect : leaves narrow (at most 3 mm. wide), shorter 
than the culm: spike oblong-ovoid to subcylindric, of 3 to 9 straw- 
colored or brownish mostly shining and ascending ovoid pointed spikelets 
0.5 to 1.5 cm. long. — Schkuhr in Willd. Sp. iv. 230, & Riedgr. 


Nachtr. 20, t. Xxx. fig. 175; Dewey, 1. c. viii. 94; Schwein. & Torr. 
1. c. 313 ; Torr. 1. c. ; Carey, 1. c. ; Boott, 1. c. iii. 116, t. 368, in part; 
Bailey, 1. c. 148, & in Gray, 1. c. ; Macouu, 1. c. 131 ; Britton, 1. c. 356, 
fig. 863 ; Howe, 48 Rep. N. Y. Mus. Nat. Hist. 42. G. leporina, 
Mich. Fl. ii. 170, not L. C. lagopodioides, var. scoparia, Boeckeler, 1. c. 
114. — Low grounds or even dry open woods, Newfoundland to 
Saskatchewan and Oregon, and southward. May- August. 

Var. moniliformis, Tuck. Spikelets scattered in a slender monili- 
form spike, the lowest usually remote. — Enum. Meth. 8, 17 ; Boott, 111. 
1. c. t. 368, in part. G. tribuloides, var. reducta, Bailey, Proc. Am. 
Acad. xxii. 147, as to syn., in part. G. tribuloides, var. moniliformis, 
Britton, 1. c. as to syn., in part. — Range of species, but infrequent. 

Var. condensa. — Fig. 5. — Spikelets spreading, crowded in a short 
globose or broad-ovoid head. — New Hampshire, Randolph, July 23, 
1897 (E. F. Williams) : Vermont, Westmore, July 26, 1894 (E. F. 
Williams); Rutland, July 14, 1899 ( W. W. Eggleston) : Massachu- 
setts, Tewksbury, July 21, 1858, Medford, July 26, 1865, Mystic 
Pond, Aug. 9, 1868, and July 20, 1873 (Wm. Boott): Rhode Island, 
Providence, July 19, 1871 (S. T. Ohiey) : Connecticutt, Griswold, 
June 16, 1899 (C. B. Graves, no. 150) : Neav York, Jefferson Co. 
(Craive) ; Fulton Chain Lakes, August, 1895 (J. V. Haberer): Ontario, 
Courtland, June 26, 1901 (John Macoun, Herb. Geol. Surv. Can., no. 

= = Perigynia 3.7 to barely 5 (average 4.5) mm. long. 

3. C. tribuloides, Wahlenb. — Figs. 6, 7. — Culms loose and usually 
tall, 0.3 to 1 m. high, sharply trigonous : leaves soft a?id loose, 3 to 8 mm. 
broad, numerous ; the upper often nearly or quite overtopping the culm ; 
those of the sterile shoots crowded and somewhat distichous : spike oblong, 
of 8 to llf. obovoid ascending more or less crowded gray-green or dull 
brown spikelets 7 to 12 mm. long: perigynia with oppressed tips. — 
Kbngl. Acad. Handl. xxiv. 145, and Fl. Lapp. 250; Bailey, Proc. Am. 
Acad. 1. c, in Gray, 1. c, & Mem. Torr. CI- i. 54 ; Macoun, 1. c. 130 ; 
Britton, 1. c. fig. 862 ; Howe, 1. c. 41. C. lagopodioides, Schkuhr in 
Willd. 1. c, & Riedgr. Nachtr. 20, t. Yyy, fig." 177 ; Dewey, 1. c. 95 ; 
Schwein. & Torr. 1. c. ; Carey, 1. c. ; Boott, 111. 1. c. t. 370; Boecke- 
ler, 1. c. 113. G. scoparia var. lagopodioides, Torr. Ann. Lye. N. Y. 
iii. 394; Tuck. 11. cc. — Swales and rich open woods, particularly in 
alluvial soil, New Brunswick to Saskatchewan, and southward. 


Var. turbata, Bailey. Spikelets remote, forming a moniliform spike. 
— Mem. Torr. CI. i. 55, & in Gray, Man, 1. c. — C. lagopodioides, var. 
Boott, 1. c. 117, t. 371, fig. 1. — Range of species. 

Var. reducta, Bailey. — Fig. 8. — Spike usually flexuous, at least 
the lowest spikelets scattered: perigynia with loosely spreading or recurred 
tips. — Proc. Am. Acad. 1. c, Mem. Torr. Cl. i. 5G, & in Gray, 1. c. ; 
Macoun, 1. c. ; Howe, 1. c. 42. C. cristata, Kunze, Car. t. 44, fig. g; 
Boott, 1. c. 117, in part, t. 373; not Schvvein. C. lagopodioides, var. 
moniliformis, Olney, Exsicc. fasc. ii. no. 8 ; Bailey, Bot. Gaz. x. 380. 
0. tribuloides, var. moniliformis, Britton, 1. c, not C. scoparia, var. 
moniliformis, Tuck. — Gulf of St. Lawrence to Nova Scotia, New 
England, New York, Iowa, and western Ontario ; ascending in 
the White Mts. to 1,385 m. altitude. 

-i- -t- Perigynia firm, not scale-like, obviously distended over the achenes. 
++ Plant strongly stoloniferous ; culms rising from an elongated rootstock. 

4. C. siccata, Dewey. — Figs. 9 to 11. — Culms slender, 1 to 6 dm. 
high ; leaves stiff, 1 to 3 mm. wide : spike of 3 to 7 approximate or scat- 
tered, glossy broivn spikelets, the staminate and pistillate flowers variously 
mixed or in distinct spikelets: perigynia 5 or 6 mm. long, 2 mm. broad, 
usually with distinct serrulate wings. — Am. Jour. Sci. x. 278, t. F. fig. 
18; Hook. Fl. Bor.-Am. ii. 212; Torr. 1. c. 391; Carey, 1. c. 539; 
Boott, 111. i. 19, t. 52; Boeckeler, 1. c. 134; Bailey, Proc. Am. Acad. 
I.e. 147, & in Gray, 1. c. 619; Macoun, 1. c. 114; Britton, 1. c. 355, 
fig. 860; Howe, 1. c. 47; Meinsh. Acta Hort. Petrop. xviii. 319. C. 
pallida, C. A. Meyer, Mem. Acad. St. Petersb. i. 215, t. 8. C. Liddoni, 
Carey, 1. c. 545, not Boott. — Dry or sandy soil, Vermont to British 
Columbia and Alaska, south to Massachusetts, Connecticut, New 
Yd*RK, Ohio, Michigan and westward. May-July. 

++ +*■ Plant not strongly stoloniferous, culms solitary or in dense stools. 

= Perigynia at most 1.4 mm. wide, elongate-lanceolate or subulate, 3.5 to 4 

(rarely 4.5) mm. long. 

a. Tips of perigynia conspicuously exceeding the lance-subulate scales : plant 
comparatively low, in dense stools. 

5. C. Crawfordii. — Figs. 12, 13. — Very slender, 1 to 3 dm. high ; 
the narrow (1 to 2.5 mm. wide) leaves ascending, often equalling or 
exceeding the culms : spike dull brown, oblong or ovoid, often subtended 
by an elongate-filiform bract; the 3 to 12 oblong or narrowly ovoid 


ascending spikelets 3 to 7 mm. long, approximate : the linear-lanceolate 
perigynia plump at base, about 1 mm. wide. — C. scoparia, var. minor, 
Boott, 111. iii. 116, t. 369; Gray, Man. ed. 5, 579; Bailey in Gray, 
Man. ed. 6, 621 ; Howe, 1. c. 43. — Dry or rocky soil, or open woods. 
Newfoundland, Whitbourne, Aug. 15, 1894 (Robinson § Schrenk, no. 
94) : Prince Edward Island, Tignish, July 20, 1888 (J. Macoun, Herb. 
Geol. Surv. Can. no. 30, 382) : New Brunswick, Nepisiquit Lakes, July, 
1884 (J. Brittain, Herb. Geol. Surv. Canada, no. 30,377) : Quebec, 
Riviere du Loup, Aug. 2, 1896, Lake Edward, Aug. 21, 1896, Tadou- 
sac, Aug. 26, 1896 (Ezra Brainerd) ; Roberval, July 27, 1892 ( G. G. 
Kennedy) : Manitoba, Lake Winnipeg, July 29, 1884 (John Macoun, 
Herb. Geol. .Surv. Can., no. 30,307, in part) : Assiniboia, Cypress 
Hills, June 25, 1894 (J. Macoun, Herb. Geol. Surv. Can., no. 7,461) 
Saskatchewan, Carleton House and Bear Lake (Sir John Richardson) 
Athabasca (Sir John Richardson, Herb. Geol. Surv. Can. no. 30, 396) 
Maine, Van Buren, July 25, 1893 (M. L. Fernald, no. 163); St. Fran- 
cis, Aug. 7, 1893, Farmington, July 8, 1896 (31. L. Fernald) ; Beech 
Mt., Mount Desert Island, Aug. 20, 1890, Somesville, July 5, 1891, 
Southwest Harbor, Aug. 1, 1892, Little Cranberry Isle, July 10, 1894, 
Seal Harbor, July 5, 1897 (E. L. Band) ; Gilead, Aug., 1897 (Kate 
Furbish) : New Hampshire, Randolph, July 23, 1897 (E. F. Wil- 
liams); near Crawfords, July 6, 1878, Mt. Washington, July 29, 1887, 
Franconia, July 6, 1878 (E. fy C. E. Faxon); Crawford Notch, 
Aug. 24, 1891, Aug. 13, 1897, and Lebanon, July 22, 1890 ( G. G. 
Kennedy): Vermont, Mt. Mansfield, July 24, 18$4 (C. W. Swan), 
Sept. 9, 1897 (E. Brainerd); Willoughby, July 21, 1896 (G. G. Ken- 
nedy); Middlebury, July 11, 1896, Ripton, July 19, 1898 (E. Brain- 
erd); Rutland, July 1, 1899 (W. W. Eggleston) : Massachusetts, 
Maiden and Revere, June 21, 1879 (H. A. Young) ; Chelsea, July 19, 
1891 (W. F. Rich): Michigan, Houghton, Sept. 15, 1871 (H. Gill- 
man) ; Keweenaw Co., Sept., 1888 (O. A. Fanvell). 

Var. vigens. — Fig. 14. — Stouter throughout: culms 3 to 6 dm. 
high : leaves 2.5 to 3 mm. broad : spikelets mostly greener, 8 to 11 mm. 
long, densely crowded in a broad-ovoid to globose head. — Thickets and 
damp gravelly soil. New Brunswick, Cam pbellton, July 20, 1880 (R. 
Chalmers, Herb. Geol. Surv. Can. no. 30,363) : Quebec, Gaspe, Aug. 
1, 1882 (John Macoun) ; Riviere du Loup, July 20 and Aug. 4, 1896, 
Lake Edward, Aug. 21, 1896 (Ezra Brainerd) : Ontario, Eastmans 
Springs, Sept. 16, 1892 (/. Macoun, Herb. Geol. Surv. Can. no. 30, 
386); Cache Lake, July 11, 1900 (John Macoun): Saskatchewan, 


plains, Aug. 1, 1872 (J. Macoun) : British Columbia, Nelson, Koote- 
nay Lake, July 3, 1890 (/. Macoun, Herb. Geol. Surv. Can., no. 30, 
393) : Maine, St. Francis, Aug. 9, 1893, Sherman, Aug. 23, 1897 
(M. L. Fernald) : New Hampshire, Randolph, Aug. 2, 1897 (E. F. 
Williams); Mt. Washington, July 28, 18G1 (Wm. Boott); Mt. Pleas- 
ant House, July 31, 1897 ( W. Deane) : Vermont, Burlington, July 
13, 1896 (JB. Brainerd): Michigan, Keweenaw Co., Aug., 1890 {0. 
A. Fa?- well). 

b. Tips of perigynia mostly equalled by the ovate blunt or acutish scales : plant 

tall, forming loose stools. 

6. C. oronensis. — Figs. 15, 16. — Culms tall and erect, 0.5 to 1 m. 
high, sharply angled and harsh above: leaves smooth, 2.5 to 4 mm. 
broad, much shorter than the culms : spike oblong-cylindric, erect, of 3 to 
9 ascending dark brown rhomboid-ovoid pointed spikelets 0.5 to 1 cm. 
long: scales mostly glossy brown, with pale scarious margins: perigynia 
appressed, about Jf. mm. long, 1.3 mm. broad, very narrowly winged above. 

— Dry fields, thickets, open woods, and gravelly banks. Maine, Orono, 
about 1870 (F. Lamson-Scribner), June 28, 1890, June 30, 1891, July 
3, 1897 (M. L. Fernald). • 

= = Perigynia 1.5 to to 2 mm. broad, ovate-lanceolate, 4.5 to 6.5 
(average 5) mm. long. 

7. C. praticola, Rydberg. — Figs. 17, 18. — Culms smooth and 
slender, 3 to 6 dm. high, overtopping the smoothish flat (2 to 3.5 mm. 
broad) leaves ; spike slender, flexuous, moniliform, the 3 to 7 silvery 
brown mostly remote pointed spikelets few-jiowered, 7 to 1.7 mm. long, 
mostly long-clavate at base ; perigynia nerveless or minutely short-nerved 
on the inner face, equalling the ovate-lanceolate acutish or blunt scales. 

— Mem. N. Y. Bot. Card. i. 84; Bvitton, Man. 226. G. pratensis, 
Drejer, Rev. Crit. Car. Bor. 24; Fl. Dan. xiv. 8, t. 2368; Bailey, 
Proc. Am. Acad. xxii. 147 ; Britton, in Britt. & Brown, 1. c. 354, fig. 
858; not Hose. C. adusta, var. minor, Boott in Hook. Fl. Bor. -Am. ii. 
215, & 111. iii. 119, t. 383. C. Liddoni, in part, of authors, not Boott. 

— Open woods, clearings, and prairies, Labrador to Saskatchewan 
and British Columbia, south to Nova Scotia, Aroostook County, 
Maine, Lake Superior, and North Dakota ; also in Greenland. 


* * Mature perigynia distinctly more than one-third (.44 to .75) as broad 

as long. 

•*- Perigynia one-fifth to one-third (.19 to .34) as thick as broad (rarely 

thicker in C. mirabilis). 

++ Mature perigynia 3 to 4 mm. long (very rarely longer in C. mirabilis and 

C. albolutescens). 

— Mature perigynia with roseate-spreading tips. 

8. C. CRISTATA, Schweinitz. — Figs. 19 to 21. — Culms 1 m. or less 
high, harsh above : leaves soft and flat, 3 to 7 mm. broad, often equalling 
the culms, sheaths loose : spike usually dense, linear-cylindric or oblong, 
of 6 to 15 globose closely flowered greenish or dull-brown spikelets 0.5 to 
1 cm. long. — Ann. Lye. N. Y. i. 66 ; Schwein. & Torr. Ann. Lye. 
N. Y. i. 315, t. 24, fig. 1 ; Dewey, 1. c. 44 ; Boott, 1. c. 117, in part ; 
Gray, Man. ed. 5, 579; Boeckeler, 1. c. 115; Howe, 1. c. 41. C. 
lagopodioides, var. cristata, Carey, 1. c. 545. C straminea, var. cristata, 
Tuck. 1. c. 9, 18. C tribuloides, var. cristata, Bailey, Proc. Am. Acad, 
xxii. 148, in Gray, Man. ed. 6, 620, & Mem. Torr. CI. i. 55 ; Macoun, 
1. c. 130. C. cristatelbi, Britton, 1. c. 357, fig. 865. — Swales and wet 
woods, western New England to Pennsylvania, " Virginia/' Mis- 
souri, Saskatchewan, and British Columbia. June-Aug. 

= = Mature perigynia with ascending tips. 

a. Plant stout and stiff: spikes stiff and upright ; the gray-green mostly approx- 
imate spikelets with appressed firm perigynia. 

9. C. albolutescens, Schweinitz. — Figs. 22 to 24. — Culms 2 to 8 
dm. high : leaves erect, long-pointed, pale green, 2 to 5 mm. wide, 
shorter than the culms : spike linear-cylindric to subglobose, with or 
without elongated bracts, of 3 to 30 (sometimes compound) conic-ovoid 
to subglobose spikelets 0.6 to 1 cm. long : perigynia 2 to 3 mm. broad, 
rhombic-ovate to suborbicular, with a short deltoid firm greenish tip. — 
Ann. Lye. N. Y. i. 66; Bailey, Bull. Torr. CI. xx. 422 (incl. var. 
cumulata) ; Britton, 1. c. 359, fig. 873; Howe, 1. c. 43. C. foenea, 
Ell. Sk. ii. 533 ; Schwein. & Torr. 1. c. 315 ; Carey, 1. c. 546; Boott, 
1. c. 118 (excl. vars.), t. 375; not Willd. C. straminea, var. foenea, 
Torr. Ann. Lye. N. Y. iii. 395 ; Bailey, Proc. Am. Acad. xxii. 150, 
& in Gray, Man. ed. 6, 622 ; Macoun, 1. c. 132. C. straminea, var. 
intermedia, Gay, Ann. Sci. Nat, ser. 2, x. 364. C. leporina, var. 
bracteata, Liebmami, Mex. Halv. 76. C. straminea, var. chlorostachys, 
Boeckeler, 1. c. 118. 0. straminea, var. cumulata, Bailey, Mem. Torr. 


CI. i. 23, & in Gray, 1. c. — Damp or even very dry soil, principally on 
the coastal plain, New Brunswick to Florida, Texas, Mexico, and 
Central America; rarely inland to Bear Mt., Livermore, Maine 
(Kate Furbish) ; Mt. Monadnock, alt. 925 in., New Hampshire (R. 
M. Harper) ; Taghkanick Range, Columbia Co., New York (L. H. 
Hoysradt) ; also from Lake Huron to Manitoba. July-Sept. 

b. Plant not very stiff : the bright green or brownish spikelets with spreading 
or ascending (not appressed) perigynia. 

1. Leaves 2.5 to G mm. wide : culms 0.3 to 1.5 m. high. 

10. C. mirabilis, Dewey. — Figs. 25, 26. — Culms very loose and 
smooth; leaves soft and thin, the sheaths rather loose : spikelets 4 to 12, 
greenish, subglobose or ovoid, 5 to 9 mm. long, mostly approximate in an 
oblong spike ; perigynia with divergent tips. — Am. Jour. Sci. xxx. 63, 
t. Bb, fig, 92; Boott, 1. c. 117 (under C. cristata), t. 374; Howe, 1. c. 
46. C. straminea, var. mirabilis, Tuck. 1. c. 9, 18; Bailey, Proc. Am. 
Acad. xxii. 150, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. 358. C. 
festucacea, var. mirabilis, Carey, 1. c. 545. C. cristata, Kunze, Car. 
t. 44, figs. a, e, and f (colored), not Schwein. C. cristata, var. mirabilis, 
Gray, Man. ed. 5, 580. C. lagopodioides, var. mirabilis, Olney, Exsicc. 
fasc. ii, no. 9. C. tribuloides, var. cristata, Macoun, 1. c. 130, in part, 
not Bailey. — Dry banks, open woods, or even moist copses, central 
Maine to Manitoba, south to North Carolina and Missouri. 
June. July. 

Var. perlonga. — Fig. 27. — Spikelets scattered in a moniliform spike. 
— New Hampshire, dry thicket, Barrett Mt., New Ipswich, June 5, 1896 
(M. L. Fernald): Vermont, Little Notch, July 9, 1901 (E. Brainerd) : 
Massachusetts, Stoueham, June 5, 1887 (F. S. Collins); Oak Island, 
Revere, July 5, 1891 (W. P. Rich); Beaver Brook Reservation, July 6, 
1894 (C. W. Swan) ; Sharon, June 17, 1896 (W. P. Rich) : Connecti- 
cut, dry open woods, Southington, June 17, 1900 (C. H. Bissell) : 
New York, Binghamton, June 29, 1871 ( Wm. Boott); Sacondago 
River (J. V. Haberer) : Michigan, Grosse Isle, June 30, 1867 (Wm. 
Boott) ; open swales, Lansing, June 8, 1886 (L. H. Bailey, no. 283, 
in part) : Illinois, Marion Co. (M. S. Bebb). 

Var. tincta. Spike of 8 to 7 ovoid approximate broion-tinged spike- 
lets : scale brown with a pale margin. — New Brunswick, banks of 
St. John River, July 4, 1899 (/. Macoun, Herb. Geol. Surv. Can. no. 
22) :. Maine, Fort Kent, June 16, 1898 (no. 2158), Masardis, June 6, 
1898 (no. 2159), Ashland, June 13, 1898 (no. 2160), Fort Fairfield, 


July 12, 1893 (no. 165), Foxcroft, June 25, 1894, Dover, June 28, 
1894, Orono, July 6, 1891,— all coll. M. L. Fernald ; Sangerville, 
July 17, 1896 (67. B. Fernald, no. 176): New Hampshire, between 
Marshfield and Fabyans, July 6, 1878, Bethlehem, June 20, 1887 {E. $ 
C. E. Faxon); Wbitefield, July 3, 1896 (W. Deane) : Vermont, St. 
Johnsbury, June 21, 1901 ( T. E. Hazen, no. 206). Resembling north- 
western forms of the polymorphous /estiva group, but not satisfactorily 
referable to any of them. 

2. Leaves 0.5 to 2 mm. wide: culms 3 to 7 dm. high : spikelets remote or at 
least distinct in a moniliform or linear-cylindric spike. 

11. C. straminea, Willd. — Figs. 28, 29. — Culms very slender, 
smooth except at summit : spikelets 3 to 8, yellow-brown, or rarely green, 
ovoid or subglobose, 4 to 8 mm. long, usually forming ftexuons spikes : 
perigynia with ascending inconspicuous tips ; the inner faces S- to 5-nerved 
or nerveless. — Willd. in Schkuhr, Riedgr. 49, t. G, fig. 34; Bailey, 
Mem. Torr. CI. i. 21, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. fig. 
868 ; Howe, I. c. 44. C. straminea, var. minor, Dewey, Am. Jour. 
Sci. xi. 318, t. N, fig. 45 ; Torr. 1. c. 395. C. festucacea, var. tenera, 
Carey, 1. c. 545. C. straminea, var. tenera, B